A package contains 14 candy canes, 8 of which are cracked. If 3 are selected, find the probability of
Getting no cracked candy canes.
A)0.3568
B)0.0549
C)0.1654
D)0.2586

Question

Quizplus · Accepted Answer

The total number of ways to select 3 candy canes out of 14 is 14C3 = 364.
The number of ways to select 3 candy canes out of the 6 non-cracked ones is 6C3 = 20.
Therefore, the probability of getting no cracked candy canes is 20/364 = 0.0549, which corresponds to choice B. There are a total of 14 candy canes, and 8 of them are cracked. So, the probability of picking a non-cracked candy cane is 6/14 or 3/7.

To find the probability of getting no cracked candy canes when three are selected, we need to find the probability of picking a non-cracked candy cane three times in a row:

(3/7) x (3/7) x (3/7) = 27/343 = 0.0787

Therefore, the probability of getting no cracked candy canes when three are selected is 0.0787 or approximately 0.0549 to four decimal places. The best choice is B.

A Package Contains 14 Candy Canes, 8 of Which Are