Suppose you conduct a series of experiments, each of which consists of tossing a fair coin 6 times. Let X be the number of heads. In each of the following questions, give your reasoning. - What are the probabilities of each value of X? - What is P(the first toss is tails | X=3)? - What is P(X = 3 | given the first toss is tails)? - What is P(the first experiment where X=5 is the eighth)? What is P( X < 5)? - What are the mean and variance of X?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Q 2(a)

Suppose you conduct a series of experiments, each of which consists of tossing a fair coin 6 times. Let X be the number of heads.

In each of the following questions, give your reasoning.

- What are the probabilities of each value of X?
- What is P(the first toss is tails | X=3)?
- What is P(X = 3 | given the first toss is tails)?
- What is P(the first experiment where X=5 is the eighth)? What is P( X < 5)?

- What are the mean and variance of X?

2.b.

Suppose one evening 6 people meet in a restaurant for dinner. They have spent the previous day apart from each other. Then later that night all 6 fall ill with food poisoning. What do you think is the most probable explanation? Explain your answer using Bayes Theorem.

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