Find the probability. Round to the nearest ten-thousandth when necessary.
-A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at Random. What is the probability that you have at least 2 orange candies?
A) 0.3362
B) 0.5758
C) 0.4909
D) 0.1515

Question

Quizplus · Accepted Answer

The probability of getting at least 2 orange candies involves calculating the probability of getting exactly 2 orange candies and the probability of getting exactly 3 orange candies, then adding those probabilities together. First, calculate the total number of ways to pick 3 candies out of 11, which is $C(11,3) = \frac{11!}{3!(11-3)!} = 165$.Next, calculate the probability of getting exactly 2 orange candies. This involves picking 2 out of the 3 orange candies and 1 out of the remaining 8 non-orange candies. The number of ways to do this is $C(3,2) \times C(8,1) = 3 \times 8 = 24$.Then, calculate the probability of getting exactly 3 orange candies. This involves picking all 3 out of the 3 orange candies, which can only be done in $C(3,3) = 1$ way.The total number of favorable outcomes is $24 + 1 = 25$.Therefore, the probability of getting at least 2 orange candies is $ \frac{25}{165} $, which simplifies to approximately 0.1515 when rounded to the nearest ten-thousandth.

Find the Probability