Question

Tanya drives to work every day and passes two dependently operated traffic lights. The probability that both lights are red is 0.35. The probability that the first light is red is 0.62. What is the probability that the second light is red, given that the first light is red?

a) 0.97
b) 0.22
c) 0.56
d) 0.27

Answer 1

To calculate the conditional probability that the second light is red given the first is red, divide the joint probability of both events by the probability of the first event. P(B|A) is approximately 0.5645, rounding to option c) 0.56.

Step-by-step explanation:

The question asks to find the probability that the second light is red, given that the first light is red. We can use the concept of conditional probability to solve this. The formula for conditional probability is P(B|A) = P(A and B) / P(A). In this scenario, A is the event that the first light is red, and B is the event that the second light is also red.

According to the information provided:

• P(A and B) = 0.35, which is the probability that both lights are red.
• P(A) = 0.62, which is the probability that the first light is red.

We calculate the conditional probability of B given A:

P(B|A) = P(A and B) / P(A) = 0.35 / 0.62 ≈ 0.5645

Therefore, the probability that the second light is red, given that the first light is red, is approximately 0.5645 or 56.45%, which is closest to the option c) 0.56.