Question 1082679
instead of finding the working scenario, let's find the not working scenarios.

we have two: (all the offspring are male) or (all the offspring are female)

Also every offspring is independet from the rest.

P(All the offspring are male) =(1/2)^4 = 1/16.

P(All the offspring are female) =(1/2)^4 = 1/16.

Using the complement

P() = 1 - (1/16+ 1/16) = 7/8.

Another way is counting all the possible scenarios:

every birth has two options, so total cases are = 2*2*2*2 = 2^4 = 16.

So the working cases are 16 - 2 = 14.

P() = (working cases) / (all cases) = 14/16 = 7/8.

Obs: do not confuse counting the cases with the calculus of the probabilities, the first way operates with probabilities, the second operates with cases and then calculates the probability.

@natolino_