Question

In government data, a household consists of all occupants of a dwelling unit. Choose an American household at random and count the number of

people it contains. Here is the assignment of probabilities for your outcome:

The probability of finding $3$people in a household is the same as the probability of finding $4$people. These probabilities are marked ??? in the table of the distribution. The probability that a household contains 3 people must be

(a) $0.68$(b) $0.32$(c) $0.16$(d) $0.08$(e) between $0$ and$1$, and we can say no more.

Short answer

The correct option is (c) 0.16

Step-by-step solution

Step 1. Given Information

The probability distribution for determining the number of people in a household is given. The chances of discovering $3$ persons in a household are the same as finding $4$people.

Step 2. Concept Used

An event is a subset of an experiment's total number of outcomes. The ratio of the number of elements in an event to the number of total outcomes is the probability of that occurrence and the use of the complimentary rule.

Step 3. Calculation 

The probabilities of $3$ and $4$ are the same.

The following are the probability distribution conditions:

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

2)The sum of all probability should equal one.

With the second condition,$$\begin{gathered} 0.25+0.32+x+x+0.07+0.03+0.01=1 \\ 2x+0.68=1 \\ 2x=0.32 \\ x=0.16 \end{gathered}$$

As a result, the likelihood of a $3$-person household is $0.16$