Chapter 0.6, Problem 12E

To determine

Probability for a comedy DVD follows 2 action DVDs, without replacement.

Answer to Problem 12E

Probability,

  $P\left(\text{2}\text{action,}\text{then}\text{a}\text{comedy}\right)=0.05$

Explanation of Solution

Given information:

DVDs on a shelf:

8 action DVDs,

3 comedy DVDs,

And

5 drama DVDs

Calculations:

Total number of DVDs are 16.

Probability for picking first action DVD,

  $P\left(\text{action}\right)=\frac{8}{16}$

When we pick first action DVD,

We have

Action DVDs decrease by 1 and total number of DVDs decrease by 1.

Probability for picking action DVD after first action DVD,

  $P\left(\text{action}|\text{action}\right)=\frac{7}{15}$

Now,

We are required to pick third DVD as comedy DVD,

In this case,

Comedy DVDs remain the same, but the total number of DVDs decrease by 2, because 2 DVDs have already been picked.

Probability for picking third comedy DVD after 2 action DVDs,

  $P\left(\text{comedy}|\left(\text{action}\text{and}\text{action}\right)\right)=\frac{3}{14}$

Thus,

We will get the probability without replacement by multiplying all the above probabilities.

  $P\left(\text{2}\text{action,}\text{then}\text{a}\text{comdey}\right)=\frac{8}{16}\cdot \frac{7}{15}\cdot \frac{3}{14}=\frac{168}{3360}=\frac{1}{20}=0.05$