You have 7 pennies, 2, nickels, and 7 dimees. Without replacement, what is the probability of choosing 2 coins that total 10 cents.

Answer 1

Hi Lisa,

We first need to figure out how many 2 coin combinations can equal 20 cents.

From

7 pennies

2 nickels

7 dimes

The only 2 coin combination that equals 20 cents is 2 dimes, which means that we need to find out the chance of picking a dime 2 times in a row.

we know that there are 7 dimes,

and there are 7 + 7 + 2 = 16 total coins,

so, the chance of picking a dime the first time is 7/16

Since we are not replacing the coins we take out,

the number of dimes and the total number of coins is reduced by one

(7 - 1) / (16 - 1)

6 / 15 = 2 / 5

Now, given that we got a dime on the first pick, the chance of getting a dime on the second pick is 2/5

If we want to pick a dime on both the first and second tries, this means that you first must win a 7/16 chance, and then a 2/5 chance. This means that you multiply the probabilities of each chance together to get the total probability of drawing 2 dimes in a row.

7/16 * 2/5 = 14/80 = 7/40

The probability of drawing 2 coins that add up to 20 cents is 7/40

Let me know if that helps!