3.4 Contingency tables and probability trees  (Page 2/6)

Muddy Mouse lives in a cage with three doors. If Muddy goes out the first door, the probability that he gets caught by Alissa the cat is $\frac{1}{5}$ and the probability he is not caught is $\frac{4}{5}$ . If he goes out the second door, the probability he gets caught by Alissa is $\frac{1}{4}$ and the probability he is not caught is $\frac{3}{4}$ . The probability that Alissa catches Muddy coming out of the third door is $\frac{1}{2}$ and the probability she does not catch Muddy is $\frac{1}{2}$ . It is equally likely that Muddy will choose any of the three doors so the probability of choosing each door is $\frac{1}{3}$ .

• The first entry $\frac{1}{15}=\left(\frac{1}{5}\right)\left(\frac{1}{3}\right)$ is $P(\text{Door One}\cap \text{Caught})$
• The entry $\frac{4}{15}=\left(\frac{4}{5}\right)\left(\frac{1}{3}\right)$ is $P(\text{Door One}\cap \text{Not Caught})$

Verify the remaining entries.

[link] contains the number of crimes per 100,000 inhabitants from 2008 to 2011 in the U.S.