You want to buy some popcorn from the concession stand but you need 20 more cents! In your pocket, you have 4 pennies, 2 nickels, and 3 dimes, if you reach in your pocket with out looking and pull out two coins, what is the probability that you will get both dimes?

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This should help you!

9 coins total, 3 dimes

drawing without replacement,
P(dime,dime) = 3/9 * 2/8

To calculate the probability of pulling out both dimes, we need to first determine the total number of possible outcomes and the number of favorable outcomes.

Total number of possible outcomes:
When reaching into your pocket without looking, you will pull out any two coins from a total of 9 coins. So the total number of possible outcomes is given by choosing 2 coins out of 9, which is denoted as C(9, 2) or 9 choose 2. This can be calculated using the combination formula as follows:

C(9, 2) = 9! / (2! * (9-2)!) = 9! / (2! * 7!) = (9 * 8) / (2 * 1) = 36

Number of favorable outcomes:
To get both dimes, you need to select 2 coins out of the 3 dimes available. Using the combination formula again:

C(3, 2) = 3! / (2! * (3-2)!) = 3! / (2! * 1!) = 3

So, the number of favorable outcomes is 3.

Therefore, the probability of pulling out both dimes is given by the ratio of the number of favorable outcomes to the total number of possible outcomes:

Probability of getting both dimes = (Number of favorable outcomes) / (Total number of possible outcomes)
= 3 / 36
= 1 / 12
≈ 0.0833 or 8.33%

Hence, the probability that you will get both dimes when pulling out two coins from your pocket without looking is approximately 8.33%.