Chapter 5.2, Problem 57E

To determine

To check the conditions of probability and tells which models are legitimate or not.

Answer to Problem 57E

The probability that household contains 3 people is 0.16

Explanation of Solution

Given:

Number of persons	1	2	3	4	5	6	7
Probability	0.25	0.32	?	?	0.07	0.03	0.01

Probability of 3 and 4 is same.

The conditions of probability distribution are:

1)The probabilities should be $0\le p\le 1$

2)Sum of all the probabilities should be 1.

Using second condition,

  $\begin{array}{l}0.25+0.32+x+x+0.07+0.03+0.01=1\\ 2x+0.68=1\\ 2x=0.32\\ x=0.16\end{array}$

Hence, probability that household contains 3 people is 0.16