Question

Artrigerator contains 5 cans of diet soda and 8 cans of regular soda. If three cans of soda are randomly selected without replacement, determine the probability that all can selected are diet soda. Use combinations to determine theprobabilityThe probability that all can selected are diet soda is(Type an integer or a simplified fraction)

Answer 1

The total number of cans in the refrigerator is 5 + 8 = 13

The number of diet soda cans is 5 while the number of regular soda cans is 8

If three cans are selected, the probability that the can is a diet soda can is

5/13

Since it was not replaced, the number of diet soda cans left would be 4 and the total number of cans left would be 12. The probability that the next selected can is a diet can is

4/12 = 1/3

Since it was not replaced, the number of diet soda cans left would be 3 and the total number of cans left would be 11. The probability that the next selected can is a diet can is

3/11

Thus, the probability that the three selected cans are diet soda cans is

5/13 * 1/3 * 3/11 = 5/143

= 0.035

the probability that the three selected cans are diet soda cans is 0.035

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