In a recent year, about $35 \%$ of all infants born in a country were conceived through in-vitro fertilization (IVF). Of the I 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) The probability that a randomly selected infant was conceived through IVF and was part of a multiple birth is 0.0 (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 0.76 . (Round to the nearest thousandth as needed.)
(c) Would it be unusual for a randomly selected IVF cycle to result in a pregnancy and produce a multiple birth? Exp below.
A. No, this is not unusual because the probability is not less than or equal to 0.05 .
B. No, this is not unusual because the probability is less than or equal to 0.05 .
C. Yes, this is unusual because the probability is not less than or equal to 0.05 .
D. Yes, this is unusual because the probability is less than or equal to 0.05 .
Answer
Since the probability of a randomly selected infant being conceived through IVF and being part of a multiple birth is greater than 0.05, it would not be considered unusual.
Step 1 ：Given that 35% of all infants born in a country were conceived through in-vitro fertilization (IVF). Let's assume that I percent of these resulted in multiple births.
Step 2 ：(a) The probability that a randomly selected infant was conceived through IVF and was part of a multiple birth would be the product of the probability of being conceived through IVF (35%) and the probability of a multiple birth given IVF (I%).
Step 3 ：(b) The probability that a randomly selected infant conceived through IVF was not part of a multiple birth would be the product of the probability of being conceived through IVF (35%) and the probability of not having a multiple birth given IVF (1-I%).
Step 4 ：(c) An event is usually considered unusual if its probability is less than or equal to 0.05. So, we would need to compare the probability calculated in part (a) with 0.05 to answer this question.
Step 5 ：Assuming I percent to be 0.2, the probability that a randomly selected infant was conceived through IVF and was part of a multiple birth is approximately \(\boxed{0.07}\).
Step 6 ：The probability that a randomly selected infant conceived through IVF was not part of a multiple birth is approximately \(\boxed{0.28}\).
Step 7 ：Since the probability of a randomly selected infant being conceived through IVF and being part of a multiple birth is greater than 0.05, it would not be considered unusual.
