Question

At a 20th high school reunion, all the classmates were asked the number of children they had. The probability of having a particular number of children was calculated from the results. Let C be the number of children reported C 0 4 P 0.05 0.14 0.34 0.24 0.11 0.07 0.02 0.02 0.01 (a) Verify that this is a probability distribution

Answer 1

a) We need to check two conditions:

1)
`\sum_(i=1)^n P_i = 1`

`0.05+0.14+0.34+0.24+0.11+0.07+0.02+0.02+0.01= 1`

2)
`P_i \geq 0 , \forall i=1,2,...,n`

So we satisfy the two conditions so then we have a probability distribution

b)
`P(C \geq 1)`

And we can use the complement rule and we got:

`P(C \geq 1)= 1-P(C<1) = 1-P(C=0)=1-0.05=0.95`

c)
`P(C=0) = 0.05`

d) For this case we see that the result from part b use the probability calculated from part c using the complement rule.

Explanation:

For this case we have the following probability distribution given:

C 0 1 2 3 4 5 6 7 8

P 0.05 0.14 0.34 0.24 0.11 0.07 0.02 0.02 0.01

And we assume the following questions:

a) Verify that this is a probability distribution

We need to check two conditions:

1)
`\sum_(i=1)^n P_i = 1`

`0.05+0.14+0.34+0.24+0.11+0.07+0.02+0.02+0.01= 1`

2)
`P_i \geq 0 , \forall i=1,2,...,n`

So we satisfy the two conditions so then we have a probability distribution

b) What is the probability one randonmly chosen classmate has at least one child

For this case we want this probability:

`P(C \geq 1)`

And we can use the complement rule and we got:

`P(C \geq 1)= 1-P(C<1) = 1-P(C=0)=1-0.05=0.95`

c) What is the probability one randonmly chosen classmate has no children

For this case we want this probability:

`P(C=0) = 0.05`

d) Look at the answers for parts b and c and explain their relationship

For this case we see that the result from part b use the probability calculated from part c using the complement rule.