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
(round to the nearest thousandth as needed.)

Explanation:

Step1: Identify the probabilities

Let \(P(IVF) = 0.34\) (probability of being conceived through IVF) and \(P(\text{multiple births}|IVF)=0.22\) (probability of multiple births given IVF).

Step2: Use the formula for conditional probability \(P(A\cap B)=P(B|A)P(A)\)

Here \(A = IVF\) and \(B=\text{multiple births}\). So \(P(IVF\cap\text{multiple births})=P(\text{multiple births}|IVF)\times P(IVF)\)
Substitute the values: \(P = 0.22\times0.34\)

$$P=0.22\times0.34=(0.2 + 0.02)\times0.34=0.2\times0.34+0.02\times0.34=0.068 + 0.0068 = 0.0748\approx0.075$$

Answer:

\(0.075\)