Question

Help please
An ice chest contains eight cans of apple​ juice, five cans of grape​ juice, seven cans of orange​ juice, and four cans of mango juice. Suppose that you reach into the container and randomly select three cans in succession. Find the probability of selecting no orange juice.

The probability of selecting no orange juice from the ice chest is ???
​(Type an integer or a simplified​ fraction.)

Answer 1

because orange juice became unpleasant when kept for long time in ice chest .

Answer 2

Given:

No. of apple juice cans = 8

No. of grape juice cans = 5

No. of orange juice cans = 7

No. of mango juice cans = 4

To find:

The probability of selecting 3 cans successively provided that none of them is orange.

Solution:

Total no. of cans = $8+5+7+4=24$

No. of ways of selecting 3 cans out of the 24 cans = $24C_{3}$

No. of cans excluding the orange juice cans = $8+5+4=17$

No. of ways of selecting 3 cans provided that none of them is orange = $17C_{3}$

Probability of selecting no orange juice = $\frac{17C_{3}}{24C_{3}}=\frac{17*16*15*14!}{3*2*14!}*\frac{3*2*21!}{24*23*22*21!} =0.33$

The probability of selecting no orange juice is 0.33