Question

An ice chest contains 7 cans of apple​ juice, 5 cans of grape​ juice, 7 cans of orange​ juice, and 5 cans of mango juice. Suppose that you reach into the container and randomly select three cans in succession. Find the probability of selecting three cans of grape juice

Answer 1

To find the probability of selecting three cans of grape juice, we need to consider the total number of ways to select three cans from the ice chest and the number of ways to select three cans of grape juice.

Total number of ways to select three cans from the ice chest = Total number of cans in the ice chest Choose 3

Total number of cans in the ice chest = 7 (apple juice) + 5 (grape juice) + 7 (orange juice) + 5 (mango juice) = 24 cans

Number of ways to select three cans of grape juice = Number of grape juice cans Choose 3 = 5 Choose 3 = 5! / (3! * (5-3)!) = 5! / (3! * 2!) = 10 ways

Now, we can calculate the probability:

Probability of selecting three cans of grape juice = (Number of ways to select three cans of grape juice) / (Total number of ways to select three cans from the ice chest)
Probability of selecting three cans of grape juice = 10 / (24 Choose 3)

Using combinations formula:
24 Choose 3 = 24! / (3! * (24-3)!) = 24! / (3! * 21!) = (24 * 23 * 22) / (3 * 2 * 1) = 2024

Probability of selecting three cans of grape juice = 10 / 2024 ≈ 0.00495

So, the probability of selecting three cans of grape juice is approximately 0.00495 or 0.495%.