Question

in a recent year, about 34% of all infants born in a country were conceived through in - vitro fertilization (ivf). of the ivf deliveries, about twenty - two 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 0.075
(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.)

Explanation:

Step1: Identify the probability of multiple births in IVF

Given that the probability of multiple births in IVF (\(P(M|IVF)\)) is \(0.22\). The probability of an infant being conceived through IVF (\(P(IVF)\)) is \(0.34\). For part (a), we used \(P(IVF\cap M)=P(IVF)\times P(M|IVF)=0.34\times0.22 = 0.0748\approx0.075\). For part (b), use the complement rule.

Step2: Apply the complement rule

The complement rule states that \(P(\overline{M}|IVF)=1 - P(M|IVF)\).
Since \(P(M|IVF) = 0.22\), then \(P(\overline{M}|IVF)=1 - 0.22\).

Answer:

\(0.780\)