The probability of having, at most, 9 girls, is 0.9515
The probability that a random baby is a girl is:
p = 0.5
And the probability that a random baby is a boy is:
q = 0.5
Then the probability that, at most, 9 out of 11 babys are girls, is given by:
1 - p(10) - p(11)
Where P(10) is the probability that 10 of the babies are girls and p(11) is the probability that the 11 babies are girls.
p(10) = C(11, 10)*(0.5)^10*(0.5)^1 = C(11, 9)*(0.5)^11
Where C(11, 10) is the combinations of 10 elements that we can make with a set of 11 elements, such that:
C(11, 10)= 11!/(11 - 10)!*10! = 11
Replacing that, we get:
P = 11*(0.5)^11 = 0.0054
p(11) = C(11, 11)*0.5^11 = 1*0.5^11 = 0.0005
Then the probability is:
P = 1 - 0.0054 - 0.0005 = 0.9515
The probability of having, at most, 9 girls, is 0.9515
If you want to learn more about probability:
https://brainly.com/question/25870256
#SPJ1
