Math 70
Spring 2014
Exam 3 Review
Exam 3 will be on Monday, May 12 and will cover Sections 8.1-8.4 and 10.3 in the book.
Below are some sample test questions you should work through before the exam. We
will review for the exam in class on Friday, May 9.
Sample Test Questions
1. Is it more likely than not that in an arbitrary group of 30 people, 2 people will
share the same birthday? Explain.
2. Assuming the probability of having a boy or a girl is the same, what’s the
probability of having all boys in a family of three kids? A family of four kids?
3. Find the probability of flipping a penny eight times and seeing at least one head.
4. You have a penny, a nickel and a die. What is the probability of flipping both
heads and rolling a 2? What is the probability of flipping a head or rolling a 2?
5. Suppose you have the 26 letters of the alphabet on separate cards in a hat. You
pick out a card, write down the letter, put the card back in the hat, mix up the
cards, pick out another card, and so on. Write an expression for the probability
that on your first six draws your letters spell HAMLET and evaluate it.
6. How many different 3 letter “words” are there (they don’t have to be real words,
just strings of 3 letters) made from a 26 letter alphabet (letters can repeat).
7. The lottery in an extremely small state consists of picking two different numbers
from 1 to 10. Ten numbered ping-pong balls are dropped into a fishbowl and two
are selected. Suppose you bet on 2 and 9 (order does not matter). What is the
probability that you win?
8. Suppose a college only offered 20 classes, none meeting at the same time, all
meeting in the same classroom, and there is no enrollment limit on any course
(they meet in a large classroom like the stadium). The college has 48,000
students and each student is required to take exactly four courses. Every student
can take any class (no prerequisites). How many different course schedules are
possible? Will some students have the exact same schedule or not? Why not?
9. Suppose you purchase $2000 worth of stock in Krispy Kreme Donuts. Three
years later, you sell your shares for $2300. If instead you had invested that
money in a three-year CD paying 5% interest compounded daily, would your
investment made you more or less money?
10. Let’s say you want to save $5,000 to put a down payment on a car loan. How
much would you have to save each month in an account earning 0.5% interest
compounded monthly in order to reach your goal in 2 years?
11. Now, let’s say you get the car loan for $30,000 (This is not the price of the car.
The car was $35,000 but you made a down payment of $5000, remember?). What
will your monthly payment be to pay back the loan in 5 years if it has a 2%
interest rate compounded monthly?
Answers to Sample Test Questions
1. More likely than not. We saw in class that in a group of 23 people, there was a
50% chance that 2 people will share a birthday and as we added more people into
the group, the probability went up.
1 1
2.
,
8 16
255
3.
= 0.996
256
1 19
4.
,
24 24
æ 1 ö6
1
5. ç ÷ =
è 26 ø 308,915,776
6. 26 3 =17,576
1
7.
45
8. 4,845 different schedules. Yes, at least 10 students must have the same schedule
by the Pigeonhole Principle (remember me?)
9. You would have made $23.64 more.
10. $19.02
11. $526.16