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A jar contains 7 pennies, 6 nickels and 8 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 X = 10. Find the probability X = 11.​

User Okie
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Answer:

Explanation:

The total number of coins in the jar is 7 + 6 + 8 = 21.

To find the probability that the sum of the values of the selected coins is 10 cents, we need to count the number of ways that we can select 2 coins such that their total value is 10 cents.

There are two ways to select two coins that have a total value of 10 cents:

Select a nickel and a dime.

Select two pennies.

The probability of selecting a nickel and a dime is (6/21) * (8/20) = 0.08, where 6/21 is the probability of selecting a nickel on the first draw, and 8/20 is the probability of selecting a dime on the second draw (without replacement).

The probability of selecting two pennies is (7/21) * (6/20) = 0.105, where 7/21 is the probability of selecting a penny on the first draw, and 6/20 is the probability of selecting a penny on the second draw (without replacement).

Therefore, the probability that the sum of the values of the selected coins is 10 cents is:

P(X = 10) = 0.08 + 0.105 = 0.185

To find the probability that the sum of the values of the selected coins is 11 cents, we need to count the number of ways that we can select 2 coins such that their total value is 11 cents.

There is only one way to select two coins that have a total value of 11 cents:

Select a nickel and a penny.

The probability of selecting a nickel and a penny is (6/21) * (7/20) = 0.07, where 6/21 is the probability of selecting a nickel on the first draw, and 7/20 is the probability of selecting a penny on the second draw (without replacement).

Therefore, the probability that the sum of the values of the selected coins is 11 cents is:

P(X = 11) = 0.07

User Toni Gamez
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