Download Ch16 Review

Binomial vs. Geometric Review
1) A 4 question pop quiz is given to you with 30 sec remaining in class. You decide not to read the questions or the 5 answer choices. You
simply select 1 answer choice/question & turn in your pop quiz to the instructor w/ 20 sec remaining in class.
Define X (random variable) to represent the number of correct answer choices.
a) What are the possible values of X?
b) Is this a binomial or geometric setting? WHY?
c) What is the probability of getting more than 2 correct answer choices?
d) What is the probability of getting at least 2 correct answer choices?
e) What is the probability of getting exactly any 2 of the 4 answer choices correct?
f) What is the probability of getting none of the 4 answer choices correct?
g) What is the probability of getting 3 or fewer of the 4 answer choices correct?
2) Eighty percent of all watches sold by a large discount store have a digital display and 20% have an analog display. The type of watch
purchased by each of the next 7 customers will be noted. Define X as the number of watches among these 7 that have a DIGITAL display.
a) Determine the probability distribution
What if Y = the number of watches among these 7 that have an analog display.
b) Determine the probability distribution
c) Find the probability that there are more than 2 digital watches out of the 7.
d) Find the probability that there are between 1 and 5 digital watches out of the 7, inclusive.
_____ 3) . A company manufactures batteries in batches of 15 and there is a 3% rate of defects. Find the mean number of defects per
batch.
A) 14.55
B) 0.435
C) 0.465
D) 3.0
E) 0.45
_____ 4) In a carnival game, a person can win a prize by guessing which 1 of 5 identical boxes contains the prize. After each guess, if the
prize has been won, a new prize is randomly placed in one of the 5 boxes. If the prize has not been won, then the prize is again randomly
placed in 1 of the 5 boxes. If a person makes 4 guesses, what is the probability that the person wins a prize exactly 2 times?
A)
2!
5!
B)
( 0 .2 ) 2
( 0 .8) 2
C) 2(0.2)(0.8)
D) (0.2)2(0.8)2
 4
E)  0.2 2 0.82
 2
_____ 5) The probability that a given eighty-year-old person will die in the next year is 0.27. What is the probability that exactly 10 out of
40 eighty-year-olds will die in the next year?
A) 0.8615
B) 0.4685
C) 0.1385
D) 0.1208
E) 0.0000000031795
_____ 6) A tennis player makes a successful first serve 48% of the time. If she serves 8 times, what is the probability that she gets
exactly 3 first serves in? Assume that each serve is independent of the others.
A) 0.0042
B) 0.7645
C) 0.2355
D) 0.1275
E) 0.1106
_____ 7) A doctor conducts blood tests on a random sample of 800 white adult men. He finds that 275 have high white blood cell counts.
Using the probability that a white adult man with a high white blood cell count contacts leukemia is 0.35, compute the expected number
of men in the sample who will contract leukemia.
A) 280
B) 275
C) 179
D) 165
E) 96
_____ 8) Pamela is playing an instant lottery game. What is the probability that she will not win until the 8th try if the probability of
winning is one out of 100 on a single try?
A) 0.0009
B) 0.0093
C) 0.0993
D) 0.9321
E) 0.9907
For each of the following identify if it as binomial, geometric or neither, then find the probability.
9) Suppose 30% of the student body is seniors. Find the probability that the first randomly selected senior student occurs on the fifth trial.
10) Your friend’s ability to shoot a success free throw (assuming your friend stands at the free throw line) is 0.2. What is the probability
that your friend finally finds success on his/her third attempt?
11) The probability that a freshman student can recover from the illness, freshmenitis, is 0.8. Suppose twenty freshmen are known to
have contracted this disease. What is the probability that exactly 12 of these sick freshmen will survive?
12) Many employers are finding that some of the people they hire are not who and what they claim to be. Detecting job applicants who
falsify their application information has spawned some new business: credential checking services. U.S. News and World Report (July 13,
1981) reported on this problem, and noted that one service found that 35% of all credentials examined were falsified. Suppose you
hire five new employees and that the probability that a single employee would falsify the information on his/her application is 0.35.
What is the probability that at least one of the five application forms has been falsified?
13) A container holds ten marbles of which five are green, two are blue, and three are red. Three marbles are to be drawn, one at a time
without replacement. What is the probability that all three marbles drawn will be green?