Question

An ice chest contains six cans of apple​ juice, eight cans of grape​ juice, four cans of orange​ juice, and two cans of mango juice. Suppose that you reach into the container and randomly select three cans in succession. Find the probability of selecting a can of grape ​juice, then a can of orange ​juice, then a can of mango

juice.

Answer 1

The probability of selecting a can of grape juice, then a can of orange juice, then a can of mango juice is 1/285.

Step-by-step explanation:

To find the probability of selecting a can of grape juice, then a can of orange juice, then a can of mango juice, we need to use the concept of conditional probability. We have a total of 6 cans of apple juice, 8 cans of grape juice, 4 cans of orange juice, and 2 cans of mango juice. The probability of selecting a can of grape juice first is 8/20, since there are 8 cans of grape juice out of a total of 20 cans. After selecting a can of grape juice, the number of cans remaining is 19, with 3 of them being orange juice. Therefore, the probability of selecting a can of orange juice next is 3/19. Lastly, after selecting a can of grape and a can of orange juice, there are 2 cans of mango juice remaining out of a total of 18 cans, so the probability of selecting a can of mango juice last is 2/18.

To find the probability of all three events happening in succession, we multiply the individual probabilities together: (8/20)(3/19)(2/18) = 1/285.