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Use the information in the Table$3.19$to answer the next eight exercises. The table shows the political party affiliation of each of localid="1649516803996" $67$members of the US Senate In June localid="1649516807155" $2012$. and when they are up freelection.

The events "Other" and "Up for reelection in November localid="1649516811372" $2016$' are

a. mutually exclusive.

b. independent.

c. both mutually exclusive and independent.

d. neither mutually exclusive nor independent

$Table3.20$gives the number of suicides estimated in the U.S. for a recent year by age, race (black or white), and sex. We are interested in possible relationships between age, race, and sex. We will let suicide victims be our population.

a. Fill in the column for the suicides for individuals over age 64.

b. Fill in the row for all other races.

c. Find the probability that a randomly selected individual was a white male.

d. Find the probability that a randomly selected individual was a black female.

e. Find the probability that a randomly selected individual was black

f. Find the probability that a randomly selected individual was a black or white male.

g. Out of the individuals over age 64, find the probability that a randomly selected individual was a black or white male.

Table 3.20 gives the number of suicides estimated in the U.S. for a recent year by age, race (black or white), and sex. We are interested in possible relationships between age, race, and sex. We will let suicide victims be our population.

a. Fill in the column for the suicides for individuals over age 64.

b. Fill in the row for all other races.

c. Find the probability that a randomly selected individual was a white male.

d. Find the probability that a randomly selected individual was a black female.

e. Find the probability that a randomly selected individual was black

f. Find the probability that a randomly selected individual was a black or white male.

g. Out of the individuals over age 64, find the probability that a randomly selected individual was a black or white

male.

Use the following information to answer the next two exercises. The table of data obtained from www.baseball-almanac.com shows hit information for four well-known baseball players. Suppose that one hit from the table is randomly selected.

Find P(hit was made by Ty Cobb|The hit was a Home Run).

a. $\frac{4189}{12351}$

b. $\frac{114}{1720}$

c. $\frac{1720}{4189}$

d. $\frac{114}{12351}$

Table 3.22 identifies a group of children by one of four hair colors, and by type of hair.

a. Complete the table.

b. What is the probability that a randomly selected child will have wavy hair?

c. What is the probability that a randomly selected child will have either brown or blond hair?

d. What is the probability that a randomly selected child will have wavy brown hair?

e. What is the probability that a randomly selected child will have red hair, given that he or she has straight hair?

f. If $B$is the event of a child having brown hair, find the probability of the complement of $B.$

g. In words, what does the complement of $B$represent?

In a previous year, the weights of the members of the San Francisco 49ers and the Dallas Cowboys were published in the San Jose Mercury News. The factual data were compiled into the following table.

For the following, suppose that you randomly select one player from the 49ers or Cowboys.

a. Find the probability that his shirt number is from 1 to 33.

b. Find the probability that he weighs at most 210 pounds.

c. Find the probability that his shirt number is from 1 to 33 AND he weighs at most 210 pounds.

d. Find the probability that his shirt number is from 1 to 33 OR he weighs at most 210 pounds.

e. Find the probability that his shirt number is from 1 to 33 GIVEN that he weighs at most 210 pounds.

Use the following information to answer the next two exercises. This tree diagram shows the tossing of an unfair coin followed by drawing one bead from a cup containing three red (R), four yellow (Y) and five blue (B) beads. For the coin, $P\left(H\right)=\frac{2}{3}$and $P\left(T\right)=\frac{1}{3}$where H is heads and T is tails.

Find P(tossing a Head on the coin AND a Red bead)

a. $\frac{2}{3}$

b. $\frac{5}{15}$

c. $\frac{6}{36}$

d. $\frac{5}{36}$

Find P(Blue bead).

a. $\frac{15}{36}$

b. $\frac{10}{36}$

c. $\frac{10}{12}$

d. $\frac{6}{36}$

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?)

a. Draw the tree that represents the possibilities for the cookie selections. Write the probabilities along each branch of the tree.

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

c. For each complete path through the tree, write the event it represents and find the probabilities.

d. Let S be the event that both cookies selected were the same flavor. Find P(S).

e. 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.

f. Let U be the event that the second cookie selected is a butter cookie. Find P(U).

A previous year, the weights of the members of the San Francisco 49ers and the Dallas Cowboys were published in the San Jose Mercury News. The factual data are compiled into $Table3.24.$

For the following, suppose that you randomly select one player from the 49ers or Cowboys. If having a shirt number from one to 33 and weighing at most 210 pounds were independent events, then what should be true about $P(Shirt\#1–33|≤210pounds)$?