The route used by a certain motorist in com mu ting to work has two intersection

Question

The route used by a certain motorist in com mu ting to work has two intersections with traffic signals. The proliability that he must stop at the first signal is 0.4. The probability that he must stop at the second signal is 0.5. The probability that he must stop at least one of the signals is 0.6. Let A = "he must stop at the first signal" and B = "he must stop at the second signal". Express the following events in terms of A and B ami find their probabilities. He must stop at both signals. He must stop at exactly one signal. He did not how to stop at the first signal but mast stop at the second one.

Explanation / Answer

Let A ="he must stop at the first signal"
B="he must stop at the second signal"
Given Probability that he must stop at the first signal=P(A)=0.4
Probability that he must stop at the second signal=P(B)=0.5
Prbability that he must stop at least one signal P(AUB)=0.6 P(A')=1-P(A)=1-0.4=0.6 P(B')=1-P(B)=1-0.5=0.5
---------------------------------------------------------------------------------------------------
a) We have to find probability that he must stop at both signals=P(AÇB)
We know that P(AUB)=P(A)+P(B)-P(AÇB) Substituting the values we get 0.6=0.4+0.5-P(AÇB) 0.6=0.9-P(AÇB) Therefore P(AÇB)=0.9-0.6=0.3 probability that he must stop at both signals=P(AÇB)=0.3 ----------------------------------------------------------------------------------------------- b)Probability that he must stop at exactly one signal =P(A'ÇB)+P(AÇB') =P(A')*P(B)+P(A)*P(B') =0.6*0.5+0.4*0.5 =0.3+0.2=0.5 Probability that he must stop at exactly one signal=0.5 ----------------------------------------------------------------------------------------------- c) Probability that he did not have to stop at the first signal but must stop at the second>ÇB) =P(A')*P(B) =0.6*0.5 =0.3 Probability that he did not have to stop at the first signal but must stop at the second ---------------------------------------------------------------------------------------------------- ----------------------------------------------------------------------------------------------------

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.