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Household size 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 the outcome. The probability of finding 3people in a household is the same as the probability of finding 4people.

a. What probability should replace 鈥?鈥 in the table? Why?

b. Find the probability that the chosen household contains more than 2people.

Short Answer

Expert verified

Part(a) 0.16 is the probability that should replace 鈥?鈥 in the table.

Part(b) 0.43 is the probability that the chosen household contains more than 2 people.

Step by step solution

01

Part(a) Step 1 : Given information

We are given a table. We need to find what probability should replace 鈥?鈥 in the table.

Number of people
1
2
3
4
5
6
7+
probability
0.25
0.32
?
?
0.07
0.03
0.01
02

Part(a) Step 2 : Simplify

As we know, Sum of all probabilities should be 1and probability should lie between 0and 1.

Let the missing probabilities be X. and both are equal.

Now,

Sum of probabilities is 0.25+0.32+x+x+0.07+0.03+0.01=12x+0.68=1x=0.16

Hence, 0.16should replace 鈥?鈥 in the table.

03

Part(b) Step 1 : Given information

We are given a table. We need to find probability that the chosen household contains more than 2people.

Number of people
1
2
3
4
5
6
7+
Probability
0.25
0.32
?
?
0.07
0.03
0.01
04

Part(b) Step 2 : Simplify

Using addition rule for disjoint events,

P(AUB)=P(A)+P(B)

Now,

Probability of 1person P(1)=0.25

Probability of 2person P(2)=0.32

Now,

P( At most 2people) =P(1)+P(2)

=0.25+0.32=0.57

Now,

Using complement rule P(Ac)=P(A)=1-P(A)

P(more than 2people ) =1-0.57=0.43

Hence, 0.43is the probability that the chosen household contains more than 2people.

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Most popular questions from this chapter

2Drive to exercise : The two-way table summarizes the responses of 120 people to a survey in which they were asked, 鈥淒o you exercise for at least 30 minutes four or more times per week?鈥 and 鈥淲hat kind of vehicle do you drive?鈥

ExerciseSedanSUVTruck
Yes251512
No202424

Suppose one person from this sample is randomly selected.

a. Find the probability that the person drives an SUV.

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If a player rolls a 2,3,or12, it is called craps. What is the probability of getting craps or an even sum on one roll of the dice?

a. 4/36

b. 18/36

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e. 32/36

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