Course: Statistics and Data Analysis

Part 1A

In the average bag of 47 pieces of Starbust candy, the following colors are expected:

Color Number

Red 5

Yellow 6

Orange 11

Green 9

Brown 2

Blue 4

Pink 10

TOTAL: 47

1. A person randomly selects one candy. What is the probability the selected candy is green?

2. A brand new bag is purchased. The person selects two candies. What is the probability that both candies are green?

3. A brand new bag is purchased. The person selects one candy. What is the probability that the candy is NOT pink?

4. A brand new bag is purchased. The person selects three candies. What is the probability that the first candy is orange, and the second candy they select is also also orange, and the third candy they select is pink?

5. A brand new bag is purchased. The person selects one candy. What is the probability that the candy is pink or blue or orange?

Part 1 B

A certain soccer player on the US Women's National team scores a goal in international play in about 24% of games that she plays in. For purposes of this question, assume that her performance in a given game is independent of her performance in any previous games.

1. If she plays in 3 games, what is the probability that she will score in all 3 games?

2. If she plays in 3 games, what is the probability that she will not score in any of the games?

3. If the plays in 3 games, what is the probability that she will score in at least (hint hint!) one of the games?

4. Thought Question: In the description to this question, I was careful to note that the athlete's performance in a given game was independent of her performance in previous games. WHy was this important to mention? That is, from a calculation perspective, if there was dependence involved (e.g. perhaps she was having confidence changes for good and bad based on her performance in previous games), what would you have needed to think about when answer the previous questions? Your answer to this does NOT have to be long. However, you do need to demonstrate an understanding of the underlying concept of dependence/independence.

Part 1C

In a certain dice game, a player realizes that they need to roll a 6 on EITHER of the two dice to win the game. So, they are going to roll 2 dice. As long as either one is a 6 they win. (This includes if both happen to be 6s).

However, if you dont get a 6 on either die, your opponent will win.

To summarize: As long as you see a 6 on either of the die, you will win, otherwise you lose. What is the probability that you will win the game?

Part 1D

This is (hopefully) an easy but interesting problem. Look up the "Monty Hall Problem". Briefly summarize the problem. Most people think that sticking with the "original door" as opposed to "switching doors" has the same probability. Why is this incorrect?

Your answer does not have to be long. But it does need to demonstrate that you have a basic understanding of what is going on.