A hospital nursery with 22 babies contains exactly 11 girls and 11 boys. If the chances of a woman giving birth to a boy or a girl are the same, what is the probability that exactly 11 out of the 22 babies are girls?
A) 0.3364
B) 0.0455
C) 0.1682
D) 0.5000
E) 0.0107

Question

A hospital nursery with 22 babies contains exactly 11 girls and 11 boys. If the chances of a woman giving birth to a boy or a girl are the same, what is the probability that exactly 11 out of the 22 babies are girls? ​
A) 0.3364
B) 0.0455
C) 0.1682
D) 0.5000
E) 0.0107

Quizplus · Accepted Answer

The probability of having a girl or a boy is 1/2 or 0.5. The number of ways to choose 11 girls out of 22 babies is given by the combination formula: 
C(22, 11) = 22! / (11! 11!) = 22 x 21 x 20 x ... x 12 / 11 x 10 x 9 x ... x 2 x 1 = 42,504
The total number of outcomes or ways to have any 11 babies out of 22 is also given by the combination formula: 
C(22, 11) = 22! / (11! 11!) = 42,504
Therefore, the probability of having exactly 11 girls out of 22 babies is:
C(11, 22) x (1/2)^22 = 42,504 x 0.5^22 = 0.1682 (rounded to four decimal places)
Therefore, the best answer choice is C.

A Hospital Nursery with 22 Babies Contains Exactly 11 Girls