Chapter 13, Problem 51SGA

(a)

To determine

To find:The probability that Reba will draw a female’s name that is not her own.

Answer to Problem 51SGA

The probability that Reba will draw a female’s name that is not her own is $\frac{7}{15}$ .

Explanation of Solution

Given:

There are 7 males and 8 females in the family.

Calculation:

Calculate the required probability.

  $P\left(R\right)=\frac{7}{15}$

Thus, the probability that at least one of the is good is $\frac{24}{25}$ .

(b)

To determine

To find:The probability that Reba will draw her own name, not replace it and then draw a male’s name.

Answer to Problem 51SGA

The probability that Reba will draw her own name, not replace it and then draw a male’s name is $\frac{1}{30}$ .

Explanation of Solution

Given:

There are 7 males and 8 females in the family.

Calculation:

Calculate the required probability.

  $\begin{array}{c}P\left(R\right)=\frac{1}{15}\frac{7}{14}\\ =\frac{1}{30}\end{array}$

Thus, the probability that Reba will draw her own name, not replace it and then draw a male’s name is $\frac{1}{30}$ .