Binomial & Geometric Distributions
Name: __________________________________
(Write next to each question whether it is Binomial or Geometric, before you answer)
1. On the SAT, there are five answer choices (A, B, C, D, and E). The probability of randomly guessing the
correct answer is .2.
a) What is the probability that on a 25-question section of the SAT by complete random guessing that
exactly 8 questions will be answered correctly?
b) What is the probability that on a 25-question section of the SAT by complete random guessing that 6 or
fewer questions will be answered correctly?
c) What is the probability that on a 25-question section of the SAT by complete random guessing that the
first correctly guessed answered is the fourth?
d) What is the probability that on a 25-question section of the SAT by complete random guessing that the
first correct answer will be within the first 6 guesses?
e) What is the expected number of correct guesses on a 25-question section of the SAT exam?
2. Will Fumble is the only receiver for LHS football team with the likelihood of catching a pass of .15.
a) What is the probability that 2 passes are caught out of 6 passes?
b) What is the probability that no passes are caught out of 6 passes?
c) What is the probability that the first pass caught is on the 1st pass?
d) What is the probability that 2 or fewer passes are caught out of 6 passes?
e) What is the probability that more than 2 passes are caught out of 6 passes?
f) What is the probability that the first pass caught is on the 4th pass?
g) What is the probability that the first pass is caught within the first 3 attempts?
h) What is the probability that the first pass is caught after the first 3 attempts?
i) What is the expect number of catches with 6 attempts?
j) What is the expect number of attempts for the first pass caught?
3. An Olympic archer is able to hit the bull’s-eye 80% of the time. Assume each shot is independent of the
others. If the archer shoots 6 arrows,
a) Define the variable X.
b) Construct a pdf (probability distribution function) table for the variable X.
c) If she shoots 6 arrows, what is the probability of each result described below.
i. Her first bull’s-eye comes on the third arrow.
ii. She misses the bull’s-eye at least once.
iii. Her first bull’s-eye comes on the fourth or fifth arrow.
iv. She gets exactly 4 bull’s-eyes.
v. She gets at least 4 bull’s-eyes.
vi. She gets at most 4 bull’s-eyes.
d) How many bull’s-eyes do you expect her to get?
e) With what standard deviation?
f) If she keeps shooting arrows until she hits the bull’s-eye, how long do you expect it will take?
4. A certain tennis player makes a successful first serve 70% of the time. Assume that each serve is independent
of the others. Suppose the tennis player serves a random number of times.
a) Find the probability that she successfully serves 68 in a match of a total of 80 serves.
b) How many would you expect her to serve before she successfully serves one in?
c) What is the probability that is takes more than 3 attempts to successfully serve one in?
d) Construct the cumulative distribution table (stop at n = 5) for the number of serves served before
successfully serving one in.