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Answer:
a) 20.95% probability of a household having 2 or 5 children.
b) 7.29% probability of a household having 3 or fewer children.
c) 19.37% probability of a household having 8 or more children.
d) 19.37% probability of a household having fewer than 5 children.
e) 92.71% probability of a household having more than 3 children.
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
In this problem, we have that:
(a) 2 or 5 children
20.95% probability of a household having 2 or 5 children.
(b) 3 or fewer children
7.29% probability of a household having 3 or fewer children.
(c) 8 or more children
19.37% probability of a household having 8 or more children.
(d) fewer than 5 children
19.37% probability of a household having fewer than 5 children.
(e) more than 3 children
Either a household has 3 or fewer children, or it has more than 3. The sum of these probabilities is 100%.
From b)
7.29% probability of a household having 3 or fewer children.
p + 7.29 = 100
p = 92.71
92.71% probability of a household having more than 3 children.