Chapter 13.4, Problem 20E

To determine

To find the probability of selecting a nickel, a dime and a quarter in that order.

Answer to Problem 20E

Dependent, $\frac{8}{195}$

Explanation of Solution

Given:

A bank contains $4$ nickels, $4$ dimes and $7$ quarters.

Calculation:

The events are dependent because outcome of one eventaffects the outcome of another event.

Let A be the event of selecting the coin and do not return.

Let B be the event of selectinganother coin and do not return.

Let C be the event of selectinganother coin.

Total sample space $=4+4+7=15$

Therefore probability of event A is $P(A)=\frac{4}{15}$

And probability of event B is $P(B)=\frac{4}{14}$

And probability of event C is $P(C)=\frac{7}{13}$

Hence,

  $\begin{array}{l}P(A\text{ and }B)=P(A)\times P(B)\times P(C)\\ P(A\text{ and }B)=\frac{4}{15}\times \frac{4}{14}\times \frac{7}{13}=\frac{8}{195}\end{array}$