Chapter 12.7, Problem 72S

a)

To determine

To find : P( $2$ rock), probability of getting $2$ rock CD's.

Answer to Problem 72S

  $\frac{\text{2}}{\text{13}}$

Explanation of Solution

Given Information :

We know that, Tine have $11$ pope, $6$ country, $16$ rock and $7$ rap CD's.

Calculation:

  $\begin{array}{l}n(s)={}^{40}{C}_2,n(\epsilon )={}^{16}{C}_2\\ p(2\text{ rock)}=\frac{{}^{16}{C}_2}{{}^{40}{C}_2}=\frac{120}{780}=\frac{4}{26}=\frac{2}{13}\end{array}$

b)

To determine

To find : P( $1$ rap), probability of getting $1$ rap CD.

Answer to Problem 72S

  $\frac{\text{7}}{\text{40}}$

Explanation of Solution

Given Information :

We know that, she has $11$ pop, $3$ country, $16$ rock and $7$ rap CD's.

Calculation:

  $n(s)={}^{40}{C}_1,n(\epsilon )={}^7{C}_1$

P(getting on rock CD) = $\frac{{}^7{C}_1}{{}^{40}{C}_1}=\frac{7}{40}$

c)

To determine

To find :P(1 rock and $1$ country)

Answer to Problem 72S

  $\frac{\text{21}}{\text{800}}$

Explanation of Solution

Given Information :

We know that, Total CD's = $11$ pop + $6$ country + $16$ rock + $7$ rap = $40$ CD's

Calculation :

P( $1$ rock and $1$ country)

P( $1$ rock) = $\frac{7}{40}$

P( $1$ country) = $\frac{6}{40}=\frac{3}{20}$

P( $1$ rock and $1$ country) = $\frac{7}{40}\cdot \frac{3}{20}=\frac{21}{800}$