Question 1082679: Find the probability that in a pig family of 4 offspring there will be at least 1 male and 1 female offspring?. Assume that the probability of a male offspring is 0.5
Answer by natolino_2017(77)   (Show Source):
You can put this solution on YOUR website! 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_
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