7. The route used by a in certain motorist commuting to work contains two inters

Question

7. The route used by a in certain motorist commuting to work contains two intersections with traffic signal is 0.4, the probability he signals. The probability that he must stop at the first that must stop at second the signal is 0.7, and the probability that he must stop at at least one of the two signals is 0.8. Let A = {he must stop at the first signal) and B = {he must stop at the second signal. Which of the following statements is true? a) A and B are mutually exclusive. b) A and B are independent c) A and B are both mutually exclusive and independent. d) A and B are neither mutually exclusive nor independent e) There is not enough information to determine which of the above statements is true.

Explanation / Answer

P(A)=0.4 and P(B)=0.7 and P(A or B)=0.8

for events to be mutually exclusive, P(A)+P(B) should be equal to P(A or B) which is not true

We see that P(A and B) which is P(A)+P(B)-P(A or B)=0.4+0.7-0.8=0.3

for events to be independent, P(A)*P(B)=P(A and B) which is not true here

Thus, D

Related Questions

Navigate

• Browse (All)
• Browse 7
• Subjects

---

---

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