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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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