Question

A man owns two old cars, A and B, and has trouble starting them on cold mornings. The probability both will start is 0.1; the probability B starts and A does not is 0.1; the probability that neither starts is 0.4 .

a) Find the probability that car A will start.

b) Find the probability that car A will start, given car B starts.

c) Find the probability that car B will start, given car A starts.

Answer 1

Probability that both card start, P(A and B) = 0.1

Probability that B starts and A does not, P(A' and B) = 0.1

Probability that both do not start, P(A' and B') = 0.4

a) P(B) = P(A and B) + P(A' and B) = 0.1+0.1 = 0.2

P(A' and B') = P((A or B)') = 0.4 (Using Demorgan's law)

P(A or B) = 1 -P(( A or B)') = 1-0.4 = 0.6

Probability that car A will start, P(A) = P(A and B) + P(A or B) - P(B)

= 0.1 + 0.6 - 0.2 = 0.5

b) Probability that car A will start, given car B starts, P(A|B) = P(A and B) / P(B)

= 0.1/0.2 = 0.5

c) Probability that car B will start, given car A starts, P(B|A) = P(A and B) / P(A)

= 0.1/0.5 = 0.2

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