Two students toss a fair coin. Whenever it lands head up, the first student wins one dollar. If not, the first student loses one dollar. Find the probability that after five coin tosses, the first student's winnings is exactly one dollar.
The first student will win exactly one dollar whenever any 3 tosses land on heads and any other 2 land on tails
So..we want to choose any 3 heads from 5 results = 5C3 = 10 ways to do this
And the number of possible outcomes is 2^5 = 32
So....the probability is 10 / 32 = 5 / 16