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?

Answer 1

0.13

0.35

0.48

0.73

Answer 2

@iGreen @midhun.madhu1987

Answer 3

Would it be A?

Answer 4

Not sure.. me too got A

Answer 5

Say \(A\) is the event that the first light is red and \(B\) is the event that the second is red.

You're given that \(P(A)=0.48\) and \(P(A\cap B)=0.35\).
\[P(B|A)=\frac{P(A\cap B)}{P(A)}=\frac{P(A)P(B)}{P(A)}=P(B)\]
where \(P(A\cap B)=P(A)P(B)\) because \(A\) and \(B\) are independent.

Use this relation to solve for \(P(B)\):
\[0.35=0.48P(B)~~\iff~~P(B)=\frac{0.35}{0.48}=0.7291\overline{6}\approx0.73\]