Question

Due to manufacturing error, three cans of regular soda were accidentally filled with diet soda and placed in a 12-pack. Suppose that two cans are randomly selected from the 12-pack: a) Determine the probability that both contain diet soda. b) Determine the probability that exactly one is diet

Answer 1

Answer:

a) 2/44 = 0.045

b) 9/22 = 0.409

Step-by-step explanation:

a) The probability the first can is diet soda is 3/12.

The probability the second can is diet soda is 2/11.

The probability of both is (3/12) (2/11) = 2/44 ≈ 0.045.

Alternatively, you can use combinations:

₃C₂ × ₉C₀ / (₁₂C₂) = 2/44

b) If the first can is diet soda, and the second can isn't, the probability is (3/12) (9/11) = 9/44.

If the first can isn't diet soda, and the second can is, the probability is (9/12) (3/11) = 9/44.

The total probability is 9/44 + 9/44 = 9/22 ≈ 0.409.

Alternatively, using combinations:

₃C₁ × ₉C₁ / (₁₂C₂) = 9/22