a fair coin is tossed 3 times,
1. what's the probability of getting two heads (exactly)?
2. what's the probability of getting three heads?
3. what's the probability of getting number of heads greater than number of tails?
Sample
Space 2 heads (exactly)? 3 heads? More heads than tails?
----------------------------------------------------------------
HHH NO YES YES
HHT YES NO YES
HTH YES NO YES
HTT NO NO NO
THH YES NO YES
THT NO NO NO
TTH NO NO NO
TTT NO NO NO
result 3 out of 8 1 out of 8 4 out of 8
P(2 heads) = 3/8
P(3 heads) = 1/8
P(more heads than tails) = 4/8 = 1/2
Also you can do this using binomial formulas:
P(2 heads) =
P(3 heads) =
P(more heads than tails) = P(2 heads OR 3 heads) = P(2 heads) + P(3 heads) = .375 + .125 = .5
Edwin