if you toss a coin in the air 3 times and catch it, what is the probability that the heads will show up exactly two times ?

Answer 1

You could use the "and/or" analogy. Since the probability of a heads is .5

Then, the probability of 2 heads is P(HHH) = P(HHT) + P(HTH) + P(THH) = .125 + .125 + .125 = .375

or you could use the combination fomula _NC_X(p)^X(q)^(N-X) where X is the number of trials, X is the number of successes, p is the probability of success, & q = 1-p

Then,

₃C₂(.5)²(.5)^(3-2) = .375