Compute Probabilities Using the General Multiplication Rule
-An ice chest contains 6 cans of apple juice, 9 cans of grape juice, 8 cans of orange juice, and 4 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) $\frac { 272 } { 975 }$
B) $\frac { 108 } { 325 }$
C) $\frac { 544 } { 2187 }$
D) $\frac { 28 } { 975 }$

Question

Quizplus · Accepted Answer

The total number of cans is 6 (apple) + 9 (grape) + 8 (orange) + 4 (pineapple) = 27 cans. To find the probability of selecting no grape juice, we consider only the cans that are not grape juice, which totals 6 + 8 + 4 = 18 cans. The probability of selecting three non-grape juice cans in succession, without replacement, is calculated using the general multiplication rule: $\frac{18}{27} \times \frac{17}{26} \times \frac{16}{25} = \frac{272}{975}$.

Compute Probabilities Using the General Multiplication Rule -An Ice Chest 272975\frac { 272 } { 975 }975272​

Compute Probabilities Using the General Multiplication Rule
-An Ice Chest $\frac { 272 } { 975 }$