In a recent year, about $35 \%$ of all infants born in a country were conceived through in-vitro fertilization (IVF). Of the IVF deliveries, about twenty-four percent resulted in multiple births. (a) Find the probability that a randomly selected infant was conceived through IVF and was part of a multiple birth. (b) Find the probability that a randomly selected infant conceived through IVF was not part of a multiple birth. (c) Would it be unusual for a randomly selected infant to have been conceived through IVF and to have been part of a multiple birth? Explain. (a) The probability that a randomly selected infant was conceived through IVF and was part of a multiple birth is 0.084 . (Round to the nearest thousandth as needed.) (b) The probability that a randomly selected infant conceived through IVF was not part of a multiple birth is (Round to the nearest thousandth as needed.)
Solution
Step 1 ：Given that the probability of an infant being conceived through IVF is 0.35 and the probability of an IVF delivery resulting in a multiple birth is 0.24.
Step 2 ：To find the probability that a randomly selected infant was conceived through IVF and was part of a multiple birth, we multiply the two probabilities. This gives us \(0.35 \times 0.24 = 0.084\).
Step 3 ：To find the probability that a randomly selected infant conceived through IVF was not part of a multiple birth, we subtract the probability of a multiple birth from 1. This gives us \(1 - 0.24 = 0.76\).
Step 4 ：Final Answer: (a) The probability that a randomly selected infant was conceived through IVF and was part of a multiple birth is approximately \(\boxed{0.084}\).
Step 5 ：(b) The probability that a randomly selected infant conceived through IVF was not part of a multiple birth is \(\boxed{0.76}\).
