Chapter 13.4, Problem 33E

To determine

To find whether the pair of events is mutually exclusive or mutually inclusive and find the probability.

Answer to Problem 33E

Mutually exclusive, $\frac{95}{165}$

Explanation of Solution

Given:

The probability at least $2$ rock from $3$ random selection from a collection of $6$ rock and $5$ rap CDs.

Calculation:

It is needed to select $2$ or $3$ rockfrom a collection of $6$ rock and $5$ rap CDs.

P (at least $2$ rock) $=$ P (selecting $2$ rock) $+$ P (selecting $3$ rock)

The events are mutually exclusive.

  $\begin{array}{l}\text{P (at least 2 rock)}=\text{P (selecting 2 rock)+P (selecting 3 rock)}\\ \text{=}\frac{C(6,2)\cdot C(5,1)}{C(11,3)}+\frac{C(6,3)\cdot C(5,0)}{C(11,3)}\\ =\frac{75}{165}+\frac{20}{165}\\ =\frac{95}{165}\end{array}$