Suppose there is a bag containing 25 envelopes and 10 of the envelopes contain prizes. You reach in, without looking, and select 2 envelopes, without replacement.
a) What is the probability that both of your picks are winner?
b) What is the probability that none of your picks is a winner?
c) what is the probability that at least one of your picks is a winner?
a) prob both winners
= (10/25)(9/24) = 3/20
b) prob both losers = (15/25)(14/24) = 7/20
c) prob of at least one winner = 1 - 7/20 = 13/20
or Prob = WL + LW + WW
= (10/25)(15/24) + (15/25)(10/24) = 3/20 = 13/20 , same as using the simple method