Question

John’s piggy bank contained 7 dimes and 3 quarters. He pulled out 1 coin without looking. Without replacing the first coin, John then pulled out a second coin.

What is the probability that both coins were dimes? Express your answer in simplest form.

Answer 1

Without replacement means that the second step depends on the results of the first.
Initially, 7 dimes and 3 quarters, total=10 coins
P(dime) = 7/10 ........... for the first draw.
For the second draw, given that he drew a dime, there are 6 dimes and 3 quarters, total 9 coins.
P(dime) = 6/9

So probability that both steps have outcome of dimes, is the product of the individual probabilities, by the product rule.