Need Help?Read t Talk to Tuter 3 points 2 E.022 Notes Ask Your T The route used

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Need Help?Read t Talk to Tuter 3 points 2 E.022 Notes Ask Your T 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 0.4, 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 o.8. a) What is the probability that he must stop at both signals? What is the probability that he must stop at the first signal but not at the second one? (e) What is the probability that he must stop at exactly one signal? Need Help? nmanLMenterl Save Home My Assignmeets Extension Request math VLC media Site 62 player oe@ Im Cortana. Ask me anything. DOLL

Explanation / Answer

Let A be Motorists stops at first signal.

B be the motorist stops at second signal.

P(A) = 0.4 , p(B) = 0.55, P( A OR B) = 0.8

a)

P(A AND B) = ?

P(A AND B) = P(A) + P(B) - P(A OR B)

= 0.4 +0.55 - 0.8

= 0.15

Probability that he must stop at both signals is 0.15

b)

P(A AND B') = P( Stops at first signal but not at second signal)

P(A AND B') = P(A) - P( A AND B)

= 0.4 - 0.15

= 0.25

The probability that he must stops at first signal but not at second one is 0.25.

C)

P( Exactly one signal) = P(A OR B) - P(A AND B)

= 0.8 - 0.15

= 0.65

The probability that he must stop at exactly one signal is 0.65.

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