S = {1, 4, 9, 16, 25, 36, 49, 64, 81, 100} is a set of 10 natural numbers. If 3 numbers are randomly picked, what is the probability that AT LEAST 2 of them are even?
5 evens, and 5 odds
prob(picking even) = 1/2, prob(picking odd) = 1/2
So it could be:
prob(exactly 2 of the 3 even) + prob(exactly 3 even)
= C(3,2) (1/2)^2 (1/2) + C(3,3) (1/2)^3
= 3/8 + 1/8
= 1/2
or
one case is EEO = (5/10)(4/9)(5/8) = 5/36
but we could have EEO, EOE, or OEE
so prob(2 of 3 evens) = 15/36= 5/12
prob(EEE) = (5/10)(4/9)(3/8) = 1/12
prob(what you said) = 6/12 = 1/2