Erika and her partner recently made the decision that they want to have a baby. Suppose that there is no biological barrier that could sabotage their plans and that Erika wants to get pregnant with the baby as soon as possible.
We know that the chance of pregnancy from intercourse is different on every day of the menstrual cycle. Erika has a 28 days cycle with a fertile window from the 9^{th} to the 15^{th} day. Outside of this fertile window her chance of getting pregnant is small (let us assume that it is zero). See the table below for the chances of pregnancy during the fertile window period.
Day |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
Chance at age 25 |
0.08 |
0.25 |
0.30 |
0.53 |
0.32 |
0.10 |
0.02 |
a. What is the probability that a randomly chosen day falls within Erika’s fertile window?
b. What is the probability that Erika becomes pregnant after “trying” on a randomly chosen day at age 25?
c. How does this number change if she is in her fertile window period?
d. To maximize their chances, the couple decides to try every day in the fertile window. What is the probability that Erika doesn’t become pregnant during the first month if she is 25?
e. At age 25, what is the probability that she does not become pregnant after three months of trying?
a.
Total fertile days = 7
Total days = 28
Probability = 7/28
= 0.25
b.
= 0.25 * Probability to get pregnant in fertile window
Probability to get pregnant in fertile window = Average of all probability
mean = E[X] = Σx*P(X) = 0.2286
= 0.25 *0.2286
= 0.0571
c.
Probability to get pregnant in fertile window = Average of all probability
mean = E[X] = Σx*P(X) = 0.2286
d. To maximize their chances, the couple decides to try every day in the fertile window. What is the probability that Erika doesn’t become pregnant during the first month if she is 25
= 1 - 0.2286
= 0.7714
e. At age 25, what is the probability that she does not become pregnant after three months of trying
= 0.7714 *0.7714* 0.7714
= 0.459
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