Two Conditional Probability Questions
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1
Every Monday, James has a math class and a biology class. The probability that he will have his math homework done is 0.42 and the probability he will have his biology homework done is 0.53. If the probability he will have his biology homework done but not his math homework is 0.29, what is the probability he will have his math homework done given that he does not have his biology done? Enter your answer as a whole number or a fraction in lowest terms.
2
J , K, and L are events in sample space S.
Pr(J)=0.44
Pr(K)=0.22
Pr(L)=0.37
Pr(J∩K)=0.12
Pr(J′∩L′)=0.39
Pr(K′∩L)=0.28
a) What is Pr(J|K)?
b) What is Pr(L|J)?
c) What is Pr(K|L′)?
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Solution Summary
Step-by-step instructions are shown in the solution, addressing conditional probability.
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1
Pr(M) = 0.42
Pr(B) = 0.53
Pr(B∩M') = 0.29
Pr(B∩M) = Pr(B) - Pr(B∩M')
= 0.53 - 0.29
= 0.24
Pr(M∩B') = Pr(M) - Pr(M∩B)
= 0.42 - 0.24
= 0.18
Pr(B') = 1 - Pr(B)
= 1 - 0.53
= 0.47
Pr(M|B') = ...
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