Question

Marley drives to work every day and passes two independently operated traffic lights. The probability that both lights are red is 0.35. The probability that the first light is red is 0.48. What is the probability that the second light is red, given that the first light is red?

a)0.13
b)0.35
c)0.48
d)0.73

Answer 1

Overall probability = Probability1 *Probability2
Using the data you already have, you can fill it in as
0.35 = 0.48 * P2
Rearrange to isolate P2, by dividing both sides by 0.48, so
0.35/0.48 = P2
P2 = 0.7291666..., which rounded to two d.p is 0.73
So d)0.73 is correct

Answer 2

Let event A be the first light being red.
Let event B be the second light being red.

P(A) = 0.48
P(A & B) = P(A) * P(B) = 0.35

P(B) = 0.35 / P(A)
P(B) = 0.35 / 0.48
P(B) = 0.73

Since the lights are independent, P(B|A) = P(B) therefore d is the correct answer.