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Chapter 6: Problem 57

A married couple plans to have four children, and they are wondering how many boys they should expect to have. Assume none of the children will be twins or other multiple births. Also assume the probability that a child will be a boy is \(0.50 .\) Explain why this is a binomial experiment. Check all four required conditions.

Short Answer

Expert verified
Yes, the scenario provided does indeed meet all four of the required conditions for a binomial experiment. The couple's plan to have four kids with an equal probability of having a boy or girl at every birth satisfies all the conditions of a binomial experiment.

Step by step solution

01

Verify the first condition

The first condition states that the experiment should be repeated a fixed number of times. Here, the couple is planning to have four children. So, this condition is satisfied.
02

Verify the second condition

The second condition states that all repetitions of the experiment must be independent. The gender of one child won't affect the gender of the next, so this condition is also met.
03

Verify the third condition

According to the third condition, there should only be two outcomes - success and failure. In this case, success could be considered having a boy, and failure could be having a girl. Hence, this condition is fulfilled.
04

Verify the fourth condition

Lastly, the fourth condition requires the probability of success to be the same for each repetition. Considering each birth as a repetition, the probability of having a boy (success) is consistently 0.5. Therefore, this too is fulfilled.

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