Question

Housing Units. Refer to Exercise 5.19.

(a) Which, if any, of the events in parts (a)-(c) are certain? impossible?

(b). Determine the probability of each event identified in part (a).

Short answer

Part (a) Part "e" is certain and part "d" is impossible

Part (b) Probabilities are 1 and 0.

Step-by-step solution

Part (a) Step 1. Given information.

The given statement is:

Refer to Exercise 5.19.

The given table in exercise 5.19 shows the number of rooms in U.S. housing units per the given table:

Rooms	No. of units
1	601
2	1,404
3	11,433
4	23,636
5	30,440
6	27,779
7	17,868
8+	19,257

Part (a) Step 2. Find which of the event is certain and impossible in parts (a)-(e) of exercise 5.19.

As we can observe If the housing unit chosen contains one or more rooms, each unit must have at least one room. Therefore, event 'e' stands for a certain event.

There is no housing unit with no room as we can see in the distribution table, Since the event housing unit selected has fewer than one room.

Therefore, 'd' event is an impossible event.

Part (b) Step 1. Determine the probability of each certain event and impossible event identified in part (a).

It is already given in the distribution table that the chosen housing units contain one or more members.

There are 132,418 housing units in all according to the given table.

We have observed that there are one or more rooms in a housing unit.

Therefore, the total number of favorable outcomes is 132,418.

The probability that the chosen housing unit contains one or more rooms is:

$$\begin{gathered} P\left(E\right)=\frac{132,418}{132,418} \\ =1 \end{gathered}$$

We can see from the distribution table that there is no housing unit that has fewer than 1 room.

Therefore, the total number of favorable outcomes will become 0.

The probability that the housing unit has fewer than 1 room. is:

$$\begin{gathered} P\left(E\right)=\frac{0}{1,32,418} \\ =0 \end{gathered}$$