Chapter 10, Problem 14CT

a.

To determine

To calculate:

The probability that you, your brother and friend are choose.

Answer to Problem 14CT

The probability that you, your brother and friend are choose is $0.16$ .

Explanation of Solution

Given information:

Random chooses volunteers $=12$

Formula used:

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

Where,

  $n=$ distinct objects,

  $r=$ time that taken objectives

Calculation:

Write the number of possible outcomes as the number of combinations of $12$ volunteers taken $3$ at a time,

  $\begin{array}{l}C{}_3=\frac{12!}{\left(12-3\right)!.3!}\\ =\frac{12\cdot 11\cdot 9!}{9!\cdot 3\cdot 2\cdot 1}\\ =220\end{array}$

Now, find the outcomes of the number of favorable outcomes. There are $C{}_2$ ways in which person concerned along with her brother and sister re chosen in summer camp.

So, the probability can be calculated as follows:

  $\begin{array}{l}P\left(personconcernedalongwithbrotherandsisterareselected\right)\\ =\frac{C{}_2}{220}\\ =\frac{36}{220}\\ =0.16\end{array}$

Hence, the probability that you, your brother and friend are choose is $0.16$ .

b.

To determine

To calculate:

The probability that you are cook, your brother is bodyguard and your friend is the counselor.

Answer to Problem 14CT

The probability that you are cook, your brother is bodyguard and your friend is the counselor is $0\cdot 03$ .

Explanation of Solution

Given information:

Random chooses volunteers $=12$

Calculation:

First, find the number of favorable outcomes. The cook can be chosen in $3$ ways, life guard can be selected $2$ ways and counselor can be chosen $1$ way.

So, the probability is calculated as follows:

  $\begin{array}{l}P\left(requiredcombination\right)=\frac{6}{220}\\ =0\cdot 03\end{array}$

Hence, the probability that you are cook, your brother is bodyguard and your friend is the counselor is $0\cdot 03$ .