Question

The route used by a certain motorist in commuting to work contains two intersections with traffic signals. The probability that he must stop at the first signal is 0.35, the analogous probability for the second signal is 0.55, and the probability that he must stop at at least one of the two signals is 0.8.

(a) What is the probability that he must stop at both signals?


(b) What is the probability that he must stop at the first signal but not at the second one?


(c) What is the probability that he must stop at exactly one signal?

Answer 1

let probability of stopping at first and second signal is A and B

hence P(A)=0.35 ; P(B)=0.55 ; P(A u B)=0.8

a)P(stop at both signs)=P(A n B)=P(A)+P(B)-P(A u B)=0.35+0.55-0.8=0.10

b)P(A n Bc) =P(A)-P(A n B)=0.35-0.10=0.25

c)P(stops at exactly one signal)=P(A u B)-P(A n B)=0.8-0.10=0.70