Chapter 12.7, Problem 18PPS

a.

To determine

To calculate: the probabilities associated with the number of students playing in at least one sport.

Explanation of Solution

Given information:

  $80\text{\%}$ of high school students have participated in at least one sport for their school.

Calculation:

(a)

The probabilities associated with the number of students who playing at least one sport is shown in following table,

$X$	$P\left(X=x\right)$
0	0.000064
1	0.001536
2	0.01536
3	0.08192
4	0.24576
5	0.393216
6	0.262144

b

To determine

To calculate: the probability that no more than 2 of the students participated in a sport

Answer to Problem 18PPS

The required probability is 0.01696

Explanation of Solution

Given information:

  $80\text{\%}$ of high school students have participated in at least one sport for their school.

Calculation:

(b)

The probability that no more than 2 of the 10 students participated in a sport is,

  $\begin{array}{cc}P(X\le 2)& ={\displaystyle \sum }_{x=0}^2\left(\begin{array}{c}6\\ x\end{array}\right){(0.80)}^x{(0.80)}^{6-x}\\ & =0.01696\end{array}$

Hence, required probability is 0.01696