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A box contains 22 pennies, 44 nickels, and 66 dimes. Six coins are drawn without replacement, with each coin having an equal probability of being chosen. What is the probability that the value of the coins drawn is at least 5050 cents

User Lzypenguin
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1 Answer

7 votes

Answer:

127/924 ≈ 0.1374

Explanation:

Given a box with 2 pennies, 4 nickels, 6 dimes, you want the probability that 6 randomly chosen coins will have a value of 50 cents or more.

50 cents

The ways 50 cents (or more) can be made from those coins are ...

  • 6 dimes
  • 5 dimes + 1 nickel
  • 5 dimes + 1 penny
  • 4 dimes + 2 nickels

Count the ways

There is 6C6 = 1 way to choose 6 dimes.

There are (6C5)(4C1) = 6·4 = 24 ways to choose 5 dimes and 1 nickel

There are (6C5)(2C1) = 6·2 = 12 ways to choose 5 dimes and 1 penny

There are (6C4)(4C2) = 15·6 = 90 ways to choose 4 dimes and 2 nickels

The total number of ways to get 50¢ or more is ...

1 +24 +12 +90 = 127

The total number of ways to choose 6 coins from the 12 is ...

12C6 = 924

Probability

The probability of choosing 6 coins that total 50¢ or more is ...

127/924 ≈ 0.1374

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A box contains 22 pennies, 44 nickels, and 66 dimes. Six coins are drawn without replacement-example-1
User Pan Ziyue
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