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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