Question

An ice chest contains 7 cans of apple juice, 9 cans of grape juice, 3 cans of orange juice, and 2 cans of pineapple juice. Suppose that you reach into the container and randomly select three cans in succession. Find the probability of selecting no grape juice.

a. 144/665
b. 6/95
c. 22/133
d. 440/3087

Answer 1

To find the probability of selecting no grape juice, we need to consider the total number of cans and the number of cans of grape juice. There are 7 cans of apple juice, 9 cans of grape juice, 3 cans of orange juice, and 2 cans of pineapple juice, for a total of 21 cans. If we randomly select three cans in succession, there are a total of 1330 possible outcomes. To select no grape juice, we need to select 3 cans that are not grape juice, so there are 220 favorable outcomes. Therefore, the probability of selecting no grape juice is 22/133.The correct answer is option c. 22/133

Step-by-step explanation:

To find the probability of selecting no grape juice, we need to consider the total number of cans and the number of cans of grape juice. There are 7 cans of apple juice, 9 cans of grape juice, 3 cans of orange juice, and 2 cans of pineapple juice, for a total of 7 + 9 + 3 + 2 = 21 cans.

If we randomly select three cans in succession, there are a total of C(21, 3) = 1330 possible outcomes. To select no grape juice, we need to select 3 cans that are not grape juice, so there are C(21-9, 3) = C(12, 3) = 220 favorable outcomes.

Therefore, the probability of selecting no grape juice is 220/1330 = 22/133.