Question

An ice chest contains 6 cans of apple​ juice,8 cans of grape​ juice,7 cans of orange​ juice, and 4 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

Given number of cans of grape juice = 8

Total number of cans = 6 + 8 + 7 + 4

= 25

Proabality that the first selected can is grape = 8/25

Probability that the second selected can is grape = 7/24 (since one grape can is already selected, we are left with 7 grape cans and total 24 cans)

Probability that the third selected can is grape = 6/23 (since two grape cans are already selected, we are left with 6 grape cans and total 23 cans)

If three events A,B and C are independent events then P(A B C) = P(A) * P(B) * P(C)

Here the selection of cans one after the other in succession is independent because selection of one can does not effect the selection of next can

So Probability of selecting three cans of grape juice = (Proabality that the first selected can is grape) * (Probability that the second selected can is grape) * (Probability that the third selected can is grape)

= (8/25) * (7/24) * (6/23)

= 336 / 13800

= 14 / 575

= 0.024348

So Probability of selecting three cans of grape juice = 14 / 575

= 0.024348