Chapter 10.5, Problem 80E

To determine

To calculate:

Probability that a person pick a black marble.

Answer to Problem 80E

Probability that a person pick a black marble is $0.2$ .

Explanation of Solution

Given information:

Bag containing $12$ white marbles, $3$ black marble.

Calculation:

Number of possible outcomes as the number of combinations of $15$ marbles taken $1$ at a time $C{}_1$ as the order is not important.

Apply combinations.

The expression for combination for $n$ objects taken $r$ at a time is given by,

  $C{}_r=\frac{n!}{\left(n-r\right)!.r!}$

The required number of combinations is given as below,

  $\begin{array}{l}C{}_1=\frac{15!}{\left(15-1\right)!.1!}\\ C{}_1=\frac{15.14!}{14!.1}\\ C{}_1=15\end{array}$

To find the number of favorable outcomes, there are $C{}_1$ ways in which $1$ black marble is chosen.

To find the probability,

  $P$ ( chosen marble is black),

  $\begin{array}{l}=\frac{C{}_1}{15}\\ =\frac{3}{15}\\ =0.2\end{array}$

Hence, Probability that a person pick a black marble is $0.2$ .