## Related questions with answers

The birth control shot is one of the most effective methods of birth control available, and it works best when you get the shot regularly, every 12 weeks. Under ideal conditions, only 1 % of women taking the shot become pregnant within one year. In typical use, however, 3% become pregnant. 7 Choose at random 20 women using the shot as their method of birth control. We count the number who become pregnant in the next year.

(a) Explain why this is a binomial setting.

(b) What is the probability that at least one of the women becomes pregnant under ideal conditions? What is the probability in typical use?

Solution

Verifieda. The four conditions for a binomial setting are: binary (success/failure), independent trials, fixed number of trials and probability of success is the same for each trial.

Binary: Satisfied, success=pregnant and failure=not pregnant

Independent trials: Satisfied, because the women were randomly selected.

Fixed number of trials: Satisfied, because we selected $n=20$ women.

Probability of success: Satisfied, because the probability of success is equal to the probability 1% under ideal conditions and 3% in typical use.

$X$ has a binomial distribution with $n=20$ and $p=1\%=0.01$, or for typical use $n=20$ and $p=3\%=0.03$.

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