This post provides additional practice for the ideas discussed in this blog post Picking Two Types of Binomial Trials.

**Problem 1**

Suppose there are two basketball players, each makes 50% of her free throws. In one game, player A attempted 10 free throws and player B attempted 15 free throws. Assume that the free throws of each player are independent of each other. Suppose you are told that in this game, 8 of their free throws were hits. Given this information:

- What is the probability that player A made 4 of the hits?
- What is the mean number of hits made by player A?
- What is the variance of the number of hits made by player A?
- What is the probability that player B made 5 of the hits?
- What is the mean number of hits made by player B?
- What is the variance of the number of hits made by player B?

**Problem 2**

A student took two multiple choice statistics quizzes that were independent of each other, i.e., results of one quiz did not affect the results on the other. One quiz had 8 questions and the other quiz had 10 questions. Each question had 5 choices and only one of the choices was correct. The student did not study. So she answered each question by random guessing. If the student was told that she had 5 correct answers in the two quizzes:

- What is the probability that the student answered 3 or more questions correctly in the first quiz?
- What is the mean number of correct answers in the first quiz?
- What is the variance of the number of correct answers in the first quiz?
- What is the probability that the student answered at most 3 questions correctly in the second quiz?
- What is the mean number of correct answers in the second quiz?
- What is the variance of the number of correct answers in the second quiz?

Refer to this post to find the background information.

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**Answers**

**Problem 1**

**Problem 2**