Question

$Table3.20$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.

Short answer

a.

b.

c. $\frac{22,050}{29,760}$

d. $\frac{330}{29,760}$

e. $\frac{2,000}{29,760}$

f. $\frac{23,720}{29,760}$

g.$\frac{5,010}{6,020}$

Step-by-step solution

Given Information

$Table3.20$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.

Explanation (part a)

The column above 64 in the table will be evaluated by subtracting the other column from the total column, we get the solution in this order as

Explanation (part b)

The row of all other peoples will be evaluated by subtracting the other row from the total rows in the table given in part a.

Explanation (part c)

the probability that a randomly selected individual was a white male:

$P(WhiteMale)=\frac{totalwhilemale}{totalnumberofpeople}=\frac{22050}{29760}$

Explanation (part d)

the probability that a randomly selected individual was a black female:

$P(Blackfemale)=\frac{totalblackfemale}{toalnumberofpeople}=\frac{330}{29760}$

Explanation (part e)

the probability that a randomly selected individual was black:

$$\begin{gathered} P\left(black\right)=P(blackmale)+P(blackfemale) \\ P\left(black\right)=\frac{1670}{29760}+\frac{330}{29760} \\ P\left(black\right)=\frac{2000}{29760} \end{gathered}$$

Explanation (part f)

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

$$\begin{gathered} P(blackmaleORwhitemale)=P(blackmale)+P(whilemale) \\ P(blackmaleORwhitemale)=\frac{1670}{29760}+\frac{22050}{29760} \\ P(blackmaleORwhitemale)=\frac{23720}{29760} \end{gathered}$$

Explanation (part g)

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

$$\begin{gathered} P(Overage64,blackmaleORwhitemale)=P(Overage64,blackmale)+P(overage64,whitemale) \\ P(Overage64,blackmaleORwhitemale)=\frac{140}{6020}+\frac{4870}{6020} \\ P(Overage64,blackmaleORwhitemale)=\frac{5010}{6020} \end{gathered}$$