Chapter CSB, Problem 4.10E

To determine

Find the probability $P\left(2actionDVDs\right)$ without replacement.

Answer to Problem 4.10E

  $\frac{7}{30}.$

Explanation of Solution

Given information:

On a shelf, there are $8$ action, $3$ comedy and $5$ chidren’s DVDs.

Assume that $2$ DVDs are selected at random.

Calculation:

Total number of outcomes are,

  $8+3+5=16$

Assume $A$ as the event when first action DVD is selected.

The possible outcomes are $8.$

So, the probability such that the first action DVD is selected is,

  $\begin{array}{l}P\left(A\right)=\frac{8}{16}\\ =\frac{1}{2}\end{array}$

Assume $B$ as the event when second action DVD is selected.

As there is no replacement and one DVD is selected, so the number of available action DVDs are $7$.

Also, the total outcome becomes $15.$

So, the probability such that the second action DVD is selected is,

  $P\left(B\right)=\frac{7}{15}.$

Multilpy the probabilities of events $AandB$ to obtain the required probability, that is,

  $\begin{array}{l}P\left(2actionDVDs\right)=P\left(A\right).P\left(B\right)\\ =\frac{1}{2}.\frac{7}{15}\\ =\frac{7}{30}\end{array}$

Hence, $P\left(2actionDVDs\right)is\frac{7}{30}.$