$U$ and $V$ are mutually exclusive events. $P(U)=0.26 ; P(V)=0.37$. Find:

$$P(U \cup V)=$$

Table 3.15 shows a random sample of musicians and how they learned to play their instruments.

$$\begin{matrix} \text{Gender} & \text{Self-taught} & \text{Studied in School} & \text{Private Instruction} & \text{Total}\\ \text{Female} & \text{12} & \text{38} & \text{22} & \text{72}\\ \text{Male} & \text{19} & \text{24} & \text{15} & \text{58}\\ \text{Total} & \text{31} & \text{62} & \text{37} & \text{130}\\ \end{matrix}$$

Find P(musician is a female).

The percentage of licensed U.S. drivers (from a recent year) that are female is $48.60$. Of the females, $5.03 \%$ are age 19 and under; $81.36 \%$ are age $20-64 ; 13.61 \%$ are age 65 or over. Of the licensed U.S. male drivers, $5.04 \%$ are age 19 and under; $81.43 \%$ are age $20-64 ; 13.53 \%$ are age 65 or over.

Complete the following.

Find $P$ (driver is age 65 or over $\cap$ female).

A and B are mutually exclusive events, with P(A) = .2 and P(B) = .3. Are A and B independent events?

Jand $K$ are independent events. $P(J \mid K)=0.3$.Find $P(J)$.

Use the following information to answer the next ten exercises. On a baseball team, there are infielders and outfielders. Some players are great hitters, and some players are not great hitters. Let I = the event that a player in an infielder. Let O = the event that a player is an outfielder. Let H = the event that a player is a great hitter. Let N = the event that a player is not a great hitter. Write the symbols for the probability that a player is not an outfielder.

If $A$ and $B$ are mutually exclusive events, with $P(A) = 0.19$ and $P(B) = 0.27$, what is $P(A$ or $B)$?

E and F are mutually exclusive events. P(E) = 0.4; P(F) = 0.5. Find P(E|F).

You are rolling a fair, six-sided number cube. Let E = the event that it lands on an even number. Let M = the event that it lands on a multiple of three. What does P(E|M) mean in words?

A and B are mutually exclusive events, with P(A) = .2 and P(B) = .3. Find P(A|B).

A box of cookies contains three chocolate and seven butter cookies. Miguel randomly selects a cookie and eats it. Then he randomly selects another cookie and eats it. (How many cookies did he take?)

Are the probabilities for the flavor of the SECOND cookie that Miguel selects independent of his first selection? Explain.

A box of cookies contains three chocolate and seven butter cookies. Miguel randomly selects a cookie and eats it. Then he randomly selects another cookie and eats it. (How many cookies did he take?)

Let $T$ be the event that the cookies selected were different flavors. Find $P(T)$ by two different methods: by using the complement rule and by using the branches of the tree. Your answers should be the same with both methods.

Flashner Marketing Research Inc.specializes in providing assessments of the prospects for women’s apparel shops in shopping malls. Al Flashner, president, reports that he assesses the prospects as good, fair, or poor. Records from previous assessments show that 60 percent of the time the prospects were rated as good, 30 percent of the time fair, and 10 percent of the time poor. Of those rated good, 80 percent made a profit the first year; of those rated fair, 60 percent made a profit the first year; and of those rated poor, 20 percent made a profit the first year. Connie’s Apparel was one of Flashner’s clients. Connie’s Apparel made a profit last year. What is the probability that it was given an original rating of poor?

$Q$ and $R$ are independent events. $P(\mathrm{Q})=0.4$ and $P(Q \cap R)=0.1$.Find $P(R)$.