2-15 A silver dollar is flipped twice. Calculate the prob[1]ability of each of the following occurring:

(A) a head on the first flip

(B) a tail on the second flip given that the first toss was a head

(C) two tails

(D) a tail on the first and a head on the second

(E) a tail on the first and a head on the second or a head on the first and a tail on the second

(F) at least one head on the two flips

2-16 An urn contains 8 red chips, 10 green chips, and 2 white chips. A chip is drawn and replaced, and then a second chip drawn. What is the probability of

(a) a white chip on the first draw?

(b) a white chip on the first draw and a red on the second?

(c) two green chips being drawn?

(d) a red chip on the second given that a white chip was drawn on the first?

2-31 What are the expected value and variance of the following probability distribution?

RANDOM VARIABLE X PROBABILITY

1 0.05

2 0.05

3 0.10

4 0.10

5 0.15

6 0.15

7 0.25

8 0.15

2-35 Trowbridge Manufacturing produces cases for per[1]sonal computers and other electronic equipment. The quality control inspector for this company believes that a particular process is out of control. Normally, only 5% of all cases are deemed defective due to discolorations. If 6 such cases are sampled, what is the probability that there will be 0 defective cases if the process is operating correctly? What is the probability that there will be exactly 1 defective case

2-38 Steve Goodman, production foreman for the Florida Gold Fruit Company, estimates that the average sale of oranges is 4,700 and the standard deviation is 500 oranges. Sales follow a normal distribution.

(A) What is the probability that sales will be greater than 5,500 oranges?

(B) What is the probability that sales will be greater than 4,500 oranges?

(C) What is the probability that sales will be less than 4,900 oranges?

(D) What is the probability that sales will be less than 4,300 oranges?

2-39 Susan Williams has been the production manager of Medical Suppliers, Inc., for the past 17 years. Medical Suppliers, Inc., is a producer of bandages and arm slings. During the past 5 years, the demand for No-Stick bandages has been fairly constant. On average, sales have been about 87,000 packages of No Stick. Susan has reason to believe that the distribution of No-Stick follows a normal curve, with a standard deviation of 4,000 packages. What is the probability that sales will be less than 81,000 packages?

2-43 Patients arrive at the emergency room of Costa Valley Hospital at an average of 5 per day. The demand for emergency room treatment at Costa Valley follows a Poisson distribution.

(A) Using Appendix C, compute the probability of exactly 0, 1, 2, 3, 4, and 5 arrivals per day.

(B) What is the sum of these probabilities, and why is the number less than 1?