1. In a lot of n components, 30% are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective,….

## What is the probability that in a sequence of 10 days, four green lights, one yellow light, and five red lights are encountered?

1 A traffic light at a certain intersection is green 50% of the time, yellow 10% of the time, and red 40% of the time. A car approaches this intersection once each day. Let X represent the number of days that pass up to and including the first time the car encounters a red light. Assume that each day represents an independent trial.

a. Find P(X = 3).

b. Find P(X ≤ 3).

c. Find µX .

d. Find σ 2 X .

2. Refer to Exercise 4. Let Y denote the number of days up to and including the third day on which a red light is encountered.

a. Find P(Y = 7).

b. Find µY .

c. Find σ 2 Y .

3. Refer to Exercise 4. What is the probability that in a sequence of 10 days, four green lights, one yellow light, and five red lights are encountered?