Question

A jar contains 6 pennies, 2 nickels and 3 dimes. A child selects 2 coins at random without replacement from the jar. Let X represent the amount in cents of the selected coins.

Find the probability when X=10.

Answer 1

To find the probability when X=10, calculate the number of favorable outcomes and divide it by the total number of possible outcomes. In this case, the probability is 4/55 or approximately 0.0727.

Step-by-step explanation:

To find the probability when X=10, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes. In this case, X represents the amount in cents of the selected coins. We have 6 pennies, 2 nickels, and 3 dimes in the jar. So, the total number of coins is 11. When two coins are selected without replacement, the number of possible outcomes is the number of ways to select 2 coins from 11, which is 11C2 = 55.

To have a sum of 10 cents, we can have either a nickel and a dime, or two nickels. The favorable outcomes are (2 nickels) and (1 nickel and 1 dime), which are 1 and 3, respectively. So, the number of favorable outcomes is 1 + 3 = 4.

Therefore, the probability when X=10 is 4/55 or approximately 0.0727.