HW 5STAT 3021
Q1. For each of these following examples, define the random variable of interest and recognize
their distributions respectively (one of the distributions learnt in class- Binomial, Multinomial,
Hypergeometric, Negative Binomial, Geometric, Poisson). Do not solve the problems in this part.
For example, you find a r.v. X given in the question follows a binomial distribution. Then you
need to specify the parameters B(n =?, p =?) according to our slides.
1. An oil company conducts a geological study that indicates that an exploratory oil well should
have a 20% chance of striking oil. What is the probability that the first strike comes on the
third well drilled?
2. Suppose you are given a 3 question multiple-choice test. Each question has 4 responses and
only one is correct. Suppose you want to find the probability that you can just guess at the
answers and get 2 questions right.
3. A crate contains 50 light bulbs of which 5 are defective and 45 are not. A Quality Control
Inspector randomly samples 4 bulbs without replacement. What is the probability that 4
bulbs are defective?
4. Let’s say that 80% of all business startups in the IT industry report that they generate a
profit in their first year. If a sample of 10 new IT business startups is selected, find the
probability that exactly seven will generate a profit in their first year.
5. Bob is a high school basketball player. He is a 70% free throw shooter. That means his
probability of making a free throw is 0.70. During the season, what is the probability that
Bob makes his third free throw on his fifth shot?
6. Your basketball team is playing a series of 5 games against your opponent. The winner is
those who wins more games (out of 5). Let assume that your team is much more skilled and
has 75% chances of winning. It means there is a 25% chance of losing. What is the probability
of your team gets 3 wins?
7. Births in a hospital occur randomly at an average rate of 1.8 births per hour. What is the
probability of observing 4 births in a given hour at the hospital?
8. Bob is a high school basketball player. He is a 70% free throw shooter. That means his
probability of making a free throw is 0.70. During the season, what is the probability that
Bob makes his first free throw on his fifth shot?
9. A box of candies has many different colors in it. There is a 15% chance of getting a pink
candy. What is the probability that exactly 4 candies in a box are pink out of 10?
10. A deck of cards contains 20 cards: 6 red cards and 14 black cards. 5 cards are drawn randomly
without replacement. What is the probability that exactly 4 red cards are drawn?
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STAT 3021
HW 5
11. In a certain town, 40% of the eligible voters prefer candidate A, 10% prefer candidate B, and
the remaining 50% have no preference. You randomly sample 10 eligible voters. What is the
probability that 4 will prefer candidate A, 1 will prefer candidate B, and the remaining 5 will
have no preference?
12. A small voting district has 101 female voters and 95 male voters. A random sample of 10
voters is drawn. What is the probability exactly 7 of the voters will be female?
13. Suppose you knew that the mean number of calls to a fire station on a weekday is 8. What
is the probability that on a given weekday there would be 11 calls?
14. An experiment of drawing a random card from an ordinary playing cards deck is done with
replacing it back. This was done ten times. Find the probability of getting 2 spades, 3
diamond, 3 club and 2 hearts.
15. It is known that 20% of products on a production line are defective. Products are inspected
until first defective is encountered. What is the probability that the first defective was found
after inspecting exactly 3 products?
16. A man was able to complete 3 files a day on an average. Find the probability that he can
complete 5 files the next day.
Q2. Answer the following questions from the book:
• Section 5.2(Binomial and multinomial): 5.4, 5.18, 5.79
• Section 5.3(Hypergeometric): 5.32, 5.40
• Section 5.4(Negative binomial and geometric): 5.90,5.91
• Section 5.5(Poisson): 5.58, 5.62, 5.68
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