Exercise 2.10

You can feel free to skip drawing a tree diagram. Whether you use the diagram or not, the key here is to condition on whether a white or red ball was put into box B from box A.

Exercise 2.22

In this problem we keep tossing coin until the first time we have an H, and then toss the coin one more time and stop. The wording is what might be confusing here. You can read the question as “find the probability that HT occurs instead of HH.” This is what is meant by HT before HH.

Exercise 2.24

The wording here might be a little misleading. The 2.38% refers to the chance of a woman aged 50 to 59 actually having cancer, and is not related to the mammography. That is \(P(\mathrm{cancer}) = 2.38%\).

Exercise 2.26

You can assume that \(P(\mbox{actually blue}) = 0.05\) and \(P(\mbox{actually yellow}) = 0.95\). About reliability, this information means \(P(\mbox{saw blue } | \mbox{ actually blue}) = P(\mbox{saw yellow } | \mbox{ actually yellow}) = 0.8\).

Exercise 2.28

You should simulate each part in R rather than computing on paper.