Round probabilities to four places. For example, 0.1234. Showyour work. For example, if you are adding two probabilities youcould do this: 7/59 + 9/59 = 16/59 = 0.2712.

1. You draw one card from a deck of 52 cards. If you get aheart, you win $18. If you get anything else, you pay $5. Note thatthere are 13 hearts in the deck.

What is the probability of winning the game?

What is the expected value of the game?

If you play the game 100 times, what is your expected gain orloss?

2. A class has sophomores and juniors, and biology and historymajors. The table below shows the number of students in eachcategory. There are 59 students in the class. (There are nodouble-majors.)

a) If one student is chosen at random, what is the probabilityof selecting a biology major?

b) If one student is chosen at random, what is the probabilityof selecting a biology major or a sophomore?

c) If two students are chosen at random, what is the probabilityof selecting a junior history major and then a sophomore biologymajor? The selections are made without replacement.

d) If one student is chosen at random, what is the probabilityof selecting a junior, given that the student chosen is a biologymajor?

e) If two students are chosen at random, what is the probabilityof selecting a sophomore history major and then another sophomorehistory major? The selections are made without replacement.

3. Find the following probabilities using the standard normaltable:

a) P(z < 1.67)

b) P(z > -1.44)

c) P(-0.87 < z < 1.95)

4. A basketball player has made 65 of 79 free-throws attempted thisseason. What is the probability that the player will make the nextfree-throw they attempt?

What is the probability that the player makes their next 10free-throws? Assume each free-throw is an independent event.

5. Horses in a stable have a mean weight of 950 pounds with astandard deviation of 77 pounds. Weights of horses follow thenormal distribution. One horse is selected at random.

a) What is the probability that the horse weighs less than 900pounds?

b) What is the probability that the horse weigh more than 1,100pounds?

c) What is the probability that the horse weighs between 900 and1,100 pounds?

d) What weight is the 90th percentile? (Round to the nearestpound)

6. Your aunt comes to you with an investment opportunity. Sheneeds you to invest $500,000. If the investment succeeds, it willpay you back your investment plus an additional $2 million. If itfails, you get nothing back. She thinks there is a 30% chance ofsuccess.

What is the expected value of the investment?

What is the most likely outcome?