Chapter 8 ­ Binomial and Geometric Distributions ­ Review Game
Round 1 ­ DO NOT WRITE ON THIS PAPER.
1) A cookbook has recipes for 10 chicken dinners, 10 beef dinners, and 15 vegetarian dinners. Pat plans dinner
by picking a recipe at random from the book. Every one of the 35 meals has an equal chance of being selected
each time Pat plans a dinner. What is the probability Pat prepares exactly 3 vegetarian dinners over 7
consecutive days?
3
15 3 20 4
b) (15
35) c) ( 35) ( 35)
a) 37
3 20 4
e) (73)(15
35) ( 35)
20
d) 3(15
35)( 35)
2) A bag contains 6 red marbles and 4 blue marbles. Ralph randomly draws a marble from the bag, notes its
color, and then replaces the marble in the bag. He remixes the marbles and repeats the process until he draws
a blue marble. What is the probability this takes Ralph more than 3 draws?
a) 0.36
b) 0.216
c) 0.167
d) 0.144
e) 0.0864
3) A baseball player has a batting average of 0.350, that is, he has a 0.350 probability of getting a hit any time he
comes to bat. If the player comes to bat four times in a game, what is the probability that the first hit occurs on
the fourth at bat?
4! (0.35)1(0.65)3
b) 3!2!
a) 1!4!
0.35
c) (0.65)
3
d) 3(0.65)(0.35)
e) (0.65)3(0.35)
4) In each of the millions of boxes of Jolly Cereal is a toy. There are five different kinds of toys of which Jimmy
has four. Jimmy wants to know how many more boxes he would expect to buy before he gets the fifth kind of
toy. Why is this NOT a binomial calculation?
a) There are five types of toys.
b) The number of boxes he will buy is not fixed.
c) The probability of getting the fifth type of toy is not 0.5.
d) The probability of getting the fifth toy is effectively constant.
e) The five types of toys are equally distributed.
5) A fair six­sided die has four faces painted green and two faces painted red. The die is rolled repeatedly until
the die lands red face up. What is the expected number of rolls until a red face is showing.
a) 1
b) 2
c) 3
d) 4
e) 6
6) An archer is able to hit the bullʹs­eye 49% of the time. If she shoots 10 arrows, what is the probability that she
gets exactly 4 bullʹs­eyes? Assume each shot is independent of the others.
a) 0.7870
b) 0.0576
c) 0.2130
d) 0.0010
e) 0.1267
Round 2 ­ DO NOT WRITE ON THIS PAPER.
7) A test consists of 10 true/false questions. If a student guesses on each question, what is the probability that
the student will answer at least 9 questions correctly.
a) 0.999
b) 0.011
c) 0.010
d) 0.001
e) 0. 9
8) Suppose a computer chip manufacturer rejects 15% of the chips produced because they fail presale testing.
If you test 4 chips, what is the probability that not all of the chips fail?
a) 5.06 × 10­4 b) 0.15
c) 0.6
d) 0.5220
e) 0.9995
9) On a multiple choice test with 13 questions, each question has four possible answers, one of which is
correct. For students who guess at all answers, find the standard deviation of the number of correct answers.
a) 1.561
b) 1.5
c) 1.875
d) 1.53
e) 1.47
10) Suppose that 19% of students at one college have high blood pressure. If you keep picking students at
random from this college, how many students do you expect to test before finding one with high blood
pressure?
a) 0.19
b) 19
c) 0.81
d) 1.23
e) 5.26
11) A basketball player has made 66% of his foul shots during the season. Assuming the shots are
independent, find the probability that in tonightʹs game he misses for the first time on his 6th attempt?
a) 0.1252
b) 0.0281
c) 0.34
d) 0.0426
e) 0.0827
12) 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) 0.465
b) 0.435
c) 14.55
d) 3.0
e) 0.45
Round 3 ­ DO NOT WRITE ON THIS PAPER.
13) A headache remedy is said to be 85% effective in curing headaches caused by simple nervous tension. An
investigator tests this remedy on 8 randomly selected patients suffering from nervous tension.
a) Find the probability that the remedy works for 7 of the patients.
b) Find the probability that the remedy works for more than 6 of the patients.
c) Find the probability that the remedy works for less than half of the patients.
d) What is the expected value for the number of people in the experiment who have success
with the remedy?
ANSWERS
1) E
2) B
3) E
4) B
5) C
6) C
7) B
8) E
9) A
10) E
11) D
12) E
13) a) 0.385
b) 0.657
2 pts for conditions (FITS/Binomial)
c) 0.003
d) 6.8
1 pt for each answer