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.

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.

kropot72 · Answer

The probability of the first coin being a dime is 7/10. If the first coin is a dime, there are 6 dimes remaining among the 9 coins that are left. So the probability of the second coin also being a dime is 6/9. Therefore required probability is given by:
$$\large P(both\ coins\ are\ dimes)=\frac{7\times6}{10\times9}=you\ can\ calculate$$