Astudy found that 3939% of the assisted reproductive technology (art) cycles resulted in pregnancies. twenty-fourfour percent of the art pregnancies resulted in multiple births. (a) find the probability that a random selected art cycle resulted in a pregnancy and produced a multiple birth. (b) find the probability that a randomly selected art cycle that resulted in a pregnancy did not produce a multiple birth. (c) would it be unusual for a randomly selected art cycle to result in a pregnancy and produce a multiple birth? explain

(a)    Let A be an ART cycle pregnancy and;B be the event that an ART cycle resulted in a multiple birth.
P(A and B) = P(A).P(B│A)
Look for P(A) and P(B│A).
P(A) = 39/100 = 0.39
P(B│A) =24/100 = 0.24
The probability that a randomly selected ART cycle resulted in a pregnancy and produced a multiple birth is P(A and B) is:
P(A and B) = P(A). P(B│A)
= 0.39 * 0.24
= 0.0936
 
(b)   Let B ’ - the complement of B. This means that this is the probability that a randomly selected ART cycle that resulted in a pregnancy did not make a multiple birth is P(B’│A).
Determine P(B’│A) using the formula the complement of an event, P(E’) = 1 – P(E), where E is an event and E’ is its complement. Recall that P(B│A) = 0.24.
P(B’│A) = 1 – P(B│A)
= 1 – 0.24
= 0.76
 (c)   Knowing that P(A and B) = 0.0936. An event that happens with a probability of 0.05 or less is normally considered unusual. Use this information to know whether it would be unusual for a randomly selected ART cycle to result in a pregnancy and produce a multiple birth. 

Angle onp = 43°angle lno = 137°angle mnp = 137°