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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What is the probability that the parcel was shipped express and arrived the next day?

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,….

Given that the test is positive, what is the probability that the person has the disease?

1.  Refer to Exercise 28. Assume that both inspectors inspect every item and that if an item has no flaw, then neither inspector will detect a flaw. a.  Assume that….

If a man tests negative, what is the probability that he actually has the disease?

1.  Refer to Example 2.26. a.  If a man tests negative, what is the probability that he actually has the disease? b.  For many medical tests, it is standard procedure….