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​These learning modules are based on the official sample problems and solutions, provided by the Society of Actuaries and Casualty Actuarial Society (that we took January 1, 2011 and used with permission). The problem set can be found here: Exam P Problem Set

Here are the solutions: Exam P Solutions

Note: The problem set may not reflect the current syllabus for the exam.

Start with:

Column “Video”- this is a short video clip (screencast) where we provide a step-by-step solution to the question
Column “Problem” –  this is the official sample question, in .pdf format
Column “Solution” –  this is the official sample solution, in .pdf format
Column “Solutions_Written”-  this is our more detailed sample solution, in .pdf format

You may also click on the Headers “Learning Objective” and “Secondary Learning Objective” to sort the problems.
If you would like a little bit more background on technical details (e.g., your calculus is rusty). There are many good sources on the internet. One great source that uses techniques and methods comparable to our site is Khan Academy.

Video 001Question 001Solution 001Solution001-writtenGeneral ProbabilityAddition and Multiplication Rules 
Video 002Question 002Solution 002Solution002-writtenGeneral ProbabilityAddition and Multiplication Rules 
Video 003Question 003Solution 003Solution003-writtenGeneral ProbabilityAddition and Multiplication Rules 
Video 004Question 004Solution 004Solution004-writtenGeneral ProbabilityAddition and Multiplication Rules 
Video 005Question 005Solution 005Solution005-writtenGeneral ProbabilityAddition and Multiplication Rules 
Video 006Question 006Solution 006Solution006-writtenGeneral ProbabilityConditional Probability 
Video 007Question 007Solution 007Solution007-writtenGeneral ProbabilityAddition and Multiplication Rules 
Video 008Question 008Solution 008Solution008-writtenGeneral Probability Addition and Multiplication Rules 
Video 009Question 009Solution 009Solution009-writtenGeneral ProbabilityAddition and Multiplication Rules 
Video 010Question 010Solution 010Solution010-writtenGeneral ProbabilityAddition and Multiplication Rules 
Video 011Question 011Solution 011Solution011-writtenGeneral ProbabilityIndependence of Events 
Video 012Question 012Solution 012Solution012-writtenGeneral ProbabilitySet Functions 
Video 013Question 013Solution 013Solution013-writtenGeneral ProbabilityConditional Probability 
Video 014Question 014Solution 014Solution014-writtenGeneral ProbabilityLaw of Total Probability 
Video 015Question 015Solution 015Solution015-writtenGeneral ProbabilityLaw of Total Probability 
Video 016Question 016Solution 016Solution016-writtenGeneral ProbabilityCombinatorial Probability 
Video 017Question 017Solution 017Solution017-writtenGeneral ProbabilityIndependence of Events 
Video 018Question 018Solution 018Solution018-writtenMultivariate Probability DistributionsProbabilities and Moments for Linear Combinations  
Video 019Question 019Solution 019General ProbabilityBayes Theorem / Law of Total Probability 
Video 020Question 020Solution 020Solution020-writtenGeneral ProbabilityBayes Theorem / Law of Total Probability 
Video 021Question 021Solution 021Solution021-writtenGeneral ProbabilityBayes Theorem / Law of Total Probability 
Video 022Question 022Solution 022Solution022-writtenGeneral ProbabilityBayes Theorem / Law of Total Probability 
Video 023Question 023Solution 023Solution023-writtenGeneral ProbabilityBayes Theorem / Law of Total Probability 
Video 024Question 024Solution 024Solution024-writtenGeneral ProbabilityConditional Probability 
Video 025Question 025Solution 025Solution025-writtenGeneral ProbabilityBayes Theorem / Law of Total Probability 
Video 026Question 026Solution 026Solution026-writtenGeneral ProbabilityBayes Theorem / Law of Total Probability 
Video 027Question 027Solution 027Solution027-writtenGeneral ProbabilityBayes Theorem / Law of Total Probability 
Video 028Question 028Solution 028Solution028-writtenGeneral ProbabilityBayes Theorem / Law of Total Probability 
Video 029Question 029Solution 029Solution029-writtenUnivariate Probability DistributionsCumulative Distribution Functions 
Video 030Question 030Solution 030Solution030-writtenUnivariate Probability DistributionsProbability Functions 
Video 031Question 031Solution 031Solution031-writtenUnivariate Probability DistributionsProbability Functions  
Video 032Question 032Solution 032Univariate Probability DistributionsProbability Functions  
Video 033Question 033Solution 033Solution033-writtenUnivariate Probability DistributionsProbability Density Functions 
Video 034Question 034Solution 034Solution034-writtenUnivariate Probability DistributionsProbability Density Functions 
Video 035Question 035Solution 035Solution035-writtenUnivariate Probability DistributionsProbability Density Functions 
Video 036Question 036Solution 036Univariate Probability DistributionsProbability Density Functions 
Video 037Question 037Solution 037Solution037-writtenUnivariate Probability DistributionsCumulative Distribution Functions 
Video 038Question 038Solution 038Univariate Probability DistributionsCumulative Distribution Functions 
Video 039Question 039Solution 039Univariate Probability DistributionsProbability Functions 
Video 040Question 040Solution 040Solution040-writtenUnivariate Probability DistributionsCumulative Distribution Functions 
Video 041Question 041Solution 041Solution041-writtenUnivariate Probability DistributionsProbability Functions 
Video 042Question 042Solution 042Solution042-writtenMultivariate Probability DistributionsProbabilities and Moments for Linear Combinations  
Video 043Question 043Solution 043Solution043-writtenUnivariate Probability DistributionsProbability Functions  
Video 044Question 044Solution 044Solution044-writtenUnivariate Probability DistributionsMoments (Expected Value) 
Video 045Question 045Solution 045Solution045-writtenUnivariate Probability DistributionsMoments (Expected Value) 
Video 046Question 046Solution 046Solution046-writtenUnivariate Probability DistributionsMoments (Expected Value) 
Video 047Question 047Solution 047Solution047-writtenUnivariate Probability DistributionsMoments (Expected Value) 
Video 048Question 048Solution 048Solution048-writtenUnivariate Probability DistributionsMoments (Expected Value) 
Video 049Question 049Solution 049Solution049-writtenUnivariate Probability DistributionsMoments (Expected Value) 
Video 050Question 050Solution 050Solution050-writtenUnivariate Probability DistributionsMoments (Expected Value) 
Video 051Question 051Solution 051Solution051-writtenUnivariate Probability DistributionsMoments (Expected Value) 
Video 052Question 052Solution 052Solution052-writtenUnivariate Probability DistributionsMoments (Expected Value) 
Video 053Question 053Solution 053Solution053-writtenUnivariate Probability DistributionsMoments (Expected Value) 
Video 054Question 054Solution 054Solution054-writtenUnivariate Probability DistributionsMoments (Expected Value) 
Video 055Question 055Solution 055Solution055-writtenUnivariate Probability DistributionsMoments (Expected Value) 
Video 056Question 056Solution 056Solution056-writtenUnivariate Probability DistributionsMoments (Expected Value) 
Video 057Question 057Solution 057Solution057-writtenUnivariate Probability DistributionsMoment Generating Functions  
Video 058Question 058Solution 058Solution058-writtenMultivariate Probability DistributionsJoint Moment Generating Functions 
Video 059Question 059Solution 059Solution059-writtenUnivariate Probability DistributionsPercentiles 
Video 060Question 060Solution 060Solution060-writtenUnivariate Probability DistributionsVariance 
Video 061Question 061Solution 061Solution061-writtenUnivariate Probability DistributionsPercentiles 
Video 062Question 062Solution 062Solution062-writtenUnivariate Probability DistributionsVariance 
Video 063Question 063Solution 063Univariate Probability DistributionsVariance 
Video 064Question 064Solution 064Solution064-writtenUnivariate Probability DistributionsVariance and Measures of Dispersion 
Video 065Question 065Solution 065Solution065-writtenUnivariate Probability DistributionsVariance and Measures of Dispersion 
Video 066Question 066Solution 066Multivariate Probability DistributionsTransformations and Order Statistics  
Video 067Question 067Solution 067Solution067-writtenUnivariate Probability DistributionsVariance and Measures of Dispersion 
Video 068Question 068Solution 068Solution068-writtenUnivariate Probability DistributionsMedian 
Video 069Question 069Solution 069Solution069-writtenUnivariate Probability DistributionsMedian 
Video 070Question 070Solution 070Solution070-writtenUnivariate Probability DistributionsPercentiles 
Video 071Question 071Solution 071Univariate Probability DistributionsTransformations 
Video 072Question 072Solution 072Solution072-writtenUnivariate Probability DistributionsTransformations 
Video 073Question 073Solution 073Solution073-writtenMultivariate Probability DistributionsTransformations 
Video 074Question 074Solution 074Solution074-writtenUnivariate Probability DistributionsTransformations 
Video 075Question 075Solution 075Solution075-writtenUnivariate Probability DistributionsTransformations 
Video 076Question 076Solution 076Multivariate Probability DistributionsTransformations and Order Statistics  
Video 077Question 077Solution 077Solution077-writtenMultivariate Probability DistributionsJoint Cumulative Distribution Functions 
Video 078Question 078Solution 078Solution078-writtenMultivariate Probability DistributionsJoint Cumulative Distribution Functions 
Video 079Question 079Solution 079Solution079-writtenMultivariate Probability DistributionsJoint Cumulative Distribution Functions 
Video 080Question 080Solution 080Multivariate Probability DistributionsCentral Limit Theorem 
Video 081Question 081Solution 081Solution081-writtenMultivariate Probability DistributionsCentral Limit Theorem 
Video 082Question 082Solution 082Multivariate Probability DistributionsCentral Limit Theorem 
Video 083Question 083Solution 083Solution083-writtenMultivariate Probability DistributionsCentral Limit Theorem 
Video 084Question 084Solution 084Multivariate Probability DistributionsCentral Limit Theorem 
Video 085Question 085Solution 085Solution085-writtenMultivariate Probability DistributionsCentral Limit Theorem 
Video 086Question 086Solution 086Solution086-writtenMultivariate Probability DistributionsCentral Limit Theorem 
Video 087Question 087Solution 087Solution087-writtenMultivariate Probability DistributionsCentral Limit Theorem 
Video 088Question 088Solution 088Multivariate Probability DistributionsJoint Cumulative Distribution Functions 
Video 089Question 089Solution 089Solution089-writtenMultivariate Probability DistributionsJoint Cumulative Distribution Functions 
Video 090Question 090Solution 090Solution090-writtenMultivariate Probability DistributionsJoint Cumulative Distribution Functions 
Video 091Question 091Solution 091Solution091-writtenMultivariate Probability DistributionsJoint Cumulative Distribution Functions 
Question 092Solution 092Multivariate Probability DistributionsJoint Cumulative Distribution Functions 
Video 093Question 093Solution 093Multivariate Probability DistributionsJoint Cumulative Distribution Functions 
Question 094Solution 094Multivariate Probability DistributionsMoments (Expected Value) 
Video 095Question 095Solution 095Solution095-writtenMultivariate Probability DistributionsJoint Moment Generating Functions 
Video 096Question 096Solution 096Solution096-writtenUnivariate Probability DistributionsMoments (Expected Value) 
Video 097Question 097Solution 097Solution097-writtenMultivariate Probability DistributionsMoments (Expected Value) for Joint Prob. Dist. 
Video 098Question 098Solution 098Solution098-writtenUnivariate Probability DistributionsMoment Generating Functions 
Video 099Question 099Solution 099Solution099-writtenMultivariate Probability DistributionsCovariance 
Video 100Question 100Solution 100Solution100-writtenMultivariate Probability DistributionsVariance for Marginal Probability Distributions  
EditVideo 101Question 101Solution 101Solution101-writtenMultivariate Probability DistributionsMoments for Linear Combinations of Independent RVs 
EditVideo 102Question 102Solution 102Solution102-writtenMultivariate Probability DistributionsMoments for Linear Combinations of Independent RVs 
EditVideo 103Question 103Solution 103Solution103-writtenMultivariate Probability DistributionsTransformations and Order Statistics  
EditQuestion 104Solution 104Multivariate Probability DistributionsCovariance 
EditVideo 105Question 105Solution 105Solution105-writtenMultivariate Probability DistributionsCovariance 
EditVideo 106Question 106Solution 106Solution106-writtenMultivariate Probability DistributionsCovariance 
EditVideo 107Question 107Solution 107Solution107-writtenMultivariate Probability DistributionsCovariance 
EditQuestion 108Solution 108Multivariate Probability DistributionsTransformations 
EditQuestion 109Solution 109Multivariate Probability DistributionsTransformations 
EditVideo 110Question 110Solution 110Solution110-writtenMultivariate Probability DistributionsConditional and Marginal Probability Distributions 
EditVideo 111Question 111Solution 111Solution111-writtenMultivariate Probability DistributionsConditional and Marginal Probability Distributions 
EditVideo 112Question 112Solution 112Solution112-writtenMultivariate Probability DistributionsConditional and Marginal Probability Distributions 
EditVideo 113Question 113Solution 113Solution113-writtenMultivariate Probability DistributionsMoments for Conditional Probability Distributions 
EditVideo 114Question 114Solution 114Solution114-writtenMultivariate Probability DistributionsVariance for Conditional Probability Distributions 
EditVideo 115Question 115Solution 115Solution115-writtenMultivariate Probability DistributionsVariance for Conditional Probability Distributions 
EditVideo 116Question 116Solution 116Solution116-writtenMultivariate Probability DistributionsVariance for Conditional Probability Distributions 
EditVideo 117Question 117Solution 117Multivariate Probability DistributionsMarginal Probability Distributions  
EditVideo 118Question 118Solution 118Solution118-writtenMultivariate Probability DistributionsMarginal Probability Distributions  
EditQuestion 119Solution 119Multivariate Probability DistributionsMarginal Probability Distributions  
EditVideo 120Question 120Solution 120Solution120-writtenMultivariate Probability DistributionsMarginal Probability Distributions  
EditVideo 121Question 121Solution 121Solution121-writtenMultivariate Probability DistributionsMoments (Expected Value) for Marginal Probability  
EditQuestion 122Solution 122Multivariate Probability DistributionsMoments (Expected Value) for Marginal Probability  
EditVideo 123Question 123Solution 123Solution123-writtenGeneral ProbabilityConditional Probability 
EditVideo 124Question 124Solution 124Solution124-writtenMultivariate Probability DistributionsVariance for Conditional Probability Distributions 
EditVideo 125Question 125Solution 125Solution125-writtenMultivariate Probability DistributionsConditional and Marginal Probability Distributions 
EditVideo 126Question 126Solution 126Solution126-writtenGeneral ProbabilityLaw of Total Probability  
EditVideo 127Question 127Solution 127Solution127-writtenMultivariate Probability DistributionsCentral Limit Theorem 
EditVideo 128Question 128Solution 128Solution128-writtenGeneral ProbabilitySet Functions incl. Set Notation and Basic Prob. 
EditVideo 129Question 129Solution 129Solution129-writtenUnivariate Probability DistributionsTransformations 
EditVideo 130Question 130Solution 130Solution130-writtenUnivariate Probability DistributionsMoment Generating Functions  
EditVideo 131Question 131Solution 131Solution131-writtenMultivariate Probability DistributionsMoments for Conditional Probability Distributions 
EditVideo 132Question 132Solution 132Solution132-writtenGeneral ProbabilityCombinatorial Probability 
EditVideo 133Question 133Solution 133Solution133-writtenUnivariate Probability DistributionsMoments (Expected Value) 
EditVideo 134Question 134Solution 134Solution134-writtenGeneral ProbabilityLaw of Total Probability  
EditVideo 135Question 135Solution 135Solution135-writtenMultivariate Probability DistributionsVariance for Marginal Probability Distributions  
EditVideo 136Question 136Solution 136Solution136-writtenMultivariate Probability DistributionsMoments for Conditional Probability Distributions 
EditVideo 137Question 137Solution 137Solution137-writtenMultivariate Probability DistributionsJoint Moment Generating Functions 
EditVideo 138Question 138Solution 138Solution138-writtenMultivariate Probability DistributionsTransformations 
EditVideo 139Question 139Solution 139Solution139-writtenMultivariate Probability DistributionsMoments for Conditional Probability Distributions 
EditVideo 140Question 140Solution 140Solution140-writtenUnivariate Probability DistributionsMode 
EditVideo 141Question 141Solution 141Solution141-writtenGeneral ProbabilityCounting Problem 
EditVideo 142Question 142Solution 142Solution142-writtenUnivariate Probability DistributionsMoments (Expected Value) 
EditVideo 143Question 143Solution 143Solution143-writtenGeneral ProbabilitySet Functions incl. Set Notation and Basic Prob. 
EditVideo 144Question 144Solution 144Multivariate Probability DistributionsJoint Cumulative Distribution Functions 
EditVideo 145Question 145Solution 145Solution145-writtenMultivariate Probability DistributionsVariance for Conditional Probability Distributions 
EditVideo 146Question 146Solution 146Solution146-writtenGeneral ProbabilitySet Functions incl. Set Notation and Basic Prob. 
EditVideo 147Question 147Solution 147Solution147-writtenUnivariate Probability DistributionsVariance 
EditVideo 148Question 148Solution 148Solution148-writtenMultivariate Probability DistributionsVariance for Marginal Probability Distributions  
EditVideo 149Question 149Solution 149Solution149-writtenMultivariate Probability DistributionsVariance for Marginal Probability Distributions  
EditVideo 150Question 150Solution 150Solution150-writtenUnivariate Probability DistributionsPercentiles 
EditVideo 151Question 151Solution 151Solution151-writtenGeneral ProbabilityCombinatorial probability 
EditVideo 152Question 152Solution 152Solution152-writtenGeneral ProbabilityConditional Probability