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Binomial Distribution Q: The sex ratio of newborn human infants is about 105 males to


New member
Dec 13, 2017

I am stuck on one of my homework problems in Stats.

The sex ratio of newborn human infants is about 105 males to 100 females. If four infants arechosen at random, what is the probability that
(a) two are male and two are female?
(b) all four are male?
(c) all four are of the same sex?

I assume you have to use the binomial distribution formula for this which is:

P(X=r) = (n/r)p^r (1-p)^(n-r)
n is the number of trials
r is the number of successes
p is the probability of success on an individual trial

So far I have n = 4, r = 2 (I have having a baby boy as the success, and girl as the failure), but im not sure how to find p.

Any hints would be greatly appreciated!


Staff member
Apr 12, 2005
Sometimes, in small experiments, it pays simply to specify the entire distribution.

Expand this: (p + q)^4

See if you can find how the formula for a single value picks out each of the five resulting elements.