Question

Question 2 (Multiple Choice Worth 6 points)

(09.03 LC)

Tanya drives to work every day and passes two independently operated traffic lights. The probability that both lights are red is 0.55. The probability that the first light is red is 0.69. What is the probability that the second light is red, given that the first light is red?
0.83
0.75
0.80
0.73

Answer 1

Given:
Probability that both lights are red 0.55
Probability that 1st light is red 0.69

Find the probability that the 2nd light is red, given that the first light is red.

0.55/0.69 = 0.797 or 0.80

The probability that the 2nd light is red while the 1st light is also red is 0.80.

Answer 2

(C) 0.80

Explanation:

Let the probability that the first light is red is=
`P_(1)` and

the probability that the second light is red=
`P_(2)`. Then,

Probability that both lights are red=
`P( P_(1) and P_(2) )`= 0.55,

Probability that the first light is red=
`P(P_(1))`=0.69,

Probability that the second light is red, given that the first light is red=
`P( P_(2) /P_(1))`=
`(P(P_(1) and P_(2)) )/(P(P_(1)) )`

=
`(0.55)/(0.69)`

=
`0.7971`

≈
`0.80`