Question

Randy has 4 pennies, 2 nickles, and 3 dimes in his pocket. If he randomly chooses 2 coins, what is the probability that they are both dimes if he doesn’t replace the first one?

Answer 1

1/12

Explanation:

This is a case of joint probability.

There are a total of (4 + 2 + 3) coins in his pocket: 9 coins.

The prob. of his choosing a dime on the first selection is 3/9, or 1/3, since there are 3 dimes out of a total of 9 coins.

Now there are 8 coins, 2 of which are dimes. The prob. of choosing a dime on the 2nd selection is 2/8, or 1/4.

The joint probability is thus (1/3)(1/4) = 1/12.

Answer 2

1/27

Explanation:

If he has 9 coins in total which gives him a 1/9 chance to pull any random coin he would also have a 1/3 chance to pull a dime from the given 9 coins. YOu multiply the likelihood of the situations together to get a final probablity of 1/27