PROBLEM 2. The route used by a driver to get to work contains two intersections

Question

PROBLEM 2. The route used by a driver to get to work contains two intersections with traffic lights. There is 35% chance that he must stop at the first traffic light, 45% chance that he must stop at the second traffic light, and 65% chance that he must stop at least one of the two traffic lights. Answer the following questions. (Hint: using Venn Diagram is very helpful, but not required). a. Find the probability that the driver must stop at both traffic lights. Answer: b. Find the probability that the driver must stop at the first traffic light but not at the second one. Answer: c. Find the probability that the driver must stop at exactly one traffic light. Answer:

Explanation / Answer

Let A denote the event of stopping at the first light and B the event of stopping at the second light.

Given P(A) = 0.35 P(B) = 0.45 P(A U B) = 0.65

a. Probability that the driver must stop at both lights = P(A B)

= P(A) + P(B) - P(A U B)

= 0.35 + 0.45 - 0.65

= 0.15.

b. Probability that the driver must stop at the first light but not the second

= P(A - B)

= P(A) - P(A B)

= 0.35 - 0.15

= 0.2

c. Probability that the driver must stop at exactly one traffic light

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

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

= 0.2 + 0.45 - 0.15

= 0.5

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