Chapter 6.1, Problem 1E

(a)

To determine

To Calculate: the event in terms of X and its probability

Answer to Problem 1E

X=5, P(X=5) =0.11

Explanation of Solution

Given:

Number of toys	0	1	2	3	4	5
Probability	0.03	0.16	0.30	0.23	0.17	???

Formula used:

  ${\displaystyle \sum \text{P}\left(X\right)=1}$

Calculation:

X=5;

  $\begin{array}{c}\because {\displaystyle \sum \text{P}\left(X\right)=1}\\ \text{P}\left(X=5\right)=1-\left\{\text{P}\left(0\right)+\text{P}\left(1\right)+\text{P}\left(2\right)+\text{P}\left(3\right)+\text{P}\left(4\right)\right\}\\ =1-\left\{0.03+0.16+0.30+0.23+0.17\right\}\\ =1-0.89\\ =0.11\end{array}$

(b)

To determine

To Calculate: the probability for at most 3

Answer to Problem 1E

  $\text{P}\left(X\le 3\right)=0.72$

Explanation of Solution

Calculation:

  $\begin{array}{c}\text{P}\left(X\le 3\right)=\text{P}\left(0\right)+\text{P}\left(1\right)+\text{P}\left(2\right)+\text{P}\left(3\right)\\ =0.03+0.16+0.30+0.23\\ =0.72\end{array}$