Question

Lazar drives to work every day and passes two independently operated traffic lights. The probability that both lights are green is 0.41. The probability that the first light is green is 0.59. What is the probability that the second light is green, given that the first light is green?. . A. 0.71. . B. 0.69. . C. 0.67. . D. 0.73

Answer 1

The probability is :

0.695 ( Option: B is the correct answer)

Explanation:

Let P denotes the probability of an event.

Let A denotes the event of first light being green.

Let B denote the event of second light being green.

Also, we are given that:

The probability that both lights are green is 0.41.

i.e. P(A∩B)=0.41

The probability that the first light is green is 0.59.

i.e. P(A)=0.59

Now, we are asked to find:

P(B|A)

We can represent this expression as:

`P(B|A)=(P(A\bigcap B))/(P(A))\\\\i.e.\\\\P(B|A)=(0.41)/(0.59)\\\\P(B|A)=0.695`

Hence, the probability of second light being green given the first light is green is:

0.695

Answer 2

Conditional probability is a measure of probability of an event given that another event has occurred.
P ( A\ B ) = P ( A ∩ B ) / P ( B ) - the conditional probability of A given B
P ( A ∩ B ) = 0.41; P ( B ) = 0.59
P ( A \ B ) = 0.41 / 0.59 = 0.6949152 ≈ 0.69
Answer: B ) 0.69