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

a) We need to check two conditions:

1)

2)

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

b)

And we can use the complement rule and we got:

c)

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

Step-by-step 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)

2)

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:

And we can use the complement rule and we got:

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

For this case we want this probability:

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.

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