Question 1150018
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A = event of solving the first problem
B = event of solving the second problem


Given 
P(A) = 0.85
P(B) = 0.45
P(A and B) = 0.05


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Part (a)


Jed has solved the second problem. So we're given that event B has happened. We want to find P(A|B) which is the probability of event A happening given B has happened.


Use the conditional probability formula
P(A|B) = P(A and B)/P(B)
P(A|B) = 0.05/0.45
P(A|B) = 0.111111
P(A|B) = 0.111


Answer: 0.111
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Part (b)


Same idea as in part (a), but now we want to find P(B|A). We know event A has happened and we want to find the probability of event B happening based on A. 


P(B|A) = P(B and A)/P(A)
P(B|A) = P(A and B)/P(A)
P(B|A) = 0.05/0.85
P(B|A) = 0.05882
P(B|A) = 0.059


Answer: 0.059
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