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 (Round to the nearest thousandth as needed.)

To solve the problem, we can calculate the probabilities based on the given information. (a) To find the probability that a randomly selected infant was conceived through IVF and was part of a multiple birth, we multiply the probability of being conceived through IVF by the probability of a multiple birth given IVF. Let: - Probability of being conceived through IVF = 35% = 0.35 - Probability of multiple births given IVF = 24% = 0.24 Now, let's calculate: \[ P(\text{IVF and Multiple Birth}) = P(\text{IVF}) \times P(\text{Multiple Birth}|\text{IVF}) = 0.35 \times 0.24 = 0.084 \] So, the probability that a randomly selected infant was conceived through IVF and part of a multiple birth is approximately \( \text{0.084} \) or \( \text{0.084} (rounded to 3 decimals). \) (b) To find the probability that a randomly selected infant conceived through IVF was not part of a multiple birth, we can subtract the probability of multiple births from 1. \[ P(\text{Not a Multiple Birth}|\text{IVF}) = 1 - P(\text{Multiple Birth}|\text{IVF}) = 1 - 0.24 = 0.76 \] So, the probability that a randomly selected infant conceived through IVF was not part of a multiple birth is \( 0.76 \). (c) To consider if it would be unusual for a randomly selected infant to have been conceived through IVF and to have been part of a multiple birth, we can look at the probability calculated in part (a), which is 0.084. In general, a probability of less than 0.05 (or 5%) is often considered unusual in statistics. Since 0.084 is greater than 0.05, it would not be considered unusual for a randomly selected infant to have been conceived through IVF and to have been part of a multiple birth. In summary: (a) Approximately \( 0.084 \) (b) \( 0.76 \) (c) Not unusual.