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?

 

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