# statistics

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two spot available and there is 6 men and 4 women what is the probability that a women will be picked?

• statistics -

number with no restriction = C(10,2) = 45

your question is ambigous, does it mean
one woman only or at least two women ?
If two women were selected, then " a woman was picked" is a true statement.
I will give both solutions:

what we don't want is all men
that would be C(6,2) = 15

prob all men = 15/45 = 1/3
so the prob of at least one woman is 1 - 1/3 = 2/3

if you want exactly one woman
number of ways = C(6,1) x C(4,1) = 24
prob of exactly one woman = 24/45 = 8/15

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