Probability problem, so confused..

[h=1]Assume that the probability of a child being a boy at birth is actually 0.478 and therefore the probability that a child is a girl at birth is 0.522. If 100 births are randomly selected, find the probability that the number of girls among the 100 babies is...[/h]A) Exactly 50

B) More than 48

c) At most 53

I just cannot figure out what type of probability this is.. I thought it was a binomial distribution but that doesn't seem to be right. Any help is appreciated, thank you.

M55 said:

Assume that the probability of a child being a boy at birth is actually 0.478 and therefore the probability that a child is a girl at birth is 0.522. If 100 births are randomly selected, find the probability that the number of girls among the 100 babies is...

A) Exactly 50

B) More than 48

c) At most 53

I just cannot figure out what type of probability this is.. I thought it was a binomial distribution but that doesn't seem to be right. Any help is appreciated, thank you.

Click to expand...

For part A, why do you say it is not binomial? Why not binomial for parts B and C. Show us your attempt at these problems and someone will surely guide you.

M55 said:

Assume that the probability of a child being a boy at birth is actually 0.478 and therefore the probability that a child is a girl at birth is 0.522. If 100 births are randomly selected, find the probability that the number of girls among the 100 babies is...
A) Exactly 50
B) More than 48
c) At most 53

Click to expand...

From the context it is not clear to me how you are expected to answer this.
We can give exact numerical answers by way of computing exact numbers.
Or we can use other methods that approximate binomial distributions.
Which are you studying?

For example: \(\displaystyle \dbinom{100}{50}(0.522)^{50}(0.478)^{50}\) will be exactly fifty. See here.
Or do we need an approximation?

\(\displaystyle \sum\limits_{k = 49}^{100} {\binom{100}{k}{{(0.522)}^k}{{(0.478)}^{100 - k}}} \) is the exact answer of the second one.