Question

In a package of M&Ms there are 20 pieces. The pieces come in 6 different colors: red, blue, green, yellow, orange and brown. Assuming that the M&M colors occur with equal probability, what is the probability of getting 5 green M&Ms in a package, using binomial distribution.

Answer 1

Answer on Question #43165-Math-Statistics and Probability

In a package of M&Ms there are 20 pieces. The pieces come in 6 different colors: red, blue, green, yellow, orange and brown. Assuming that the M&M colors occur with equal probability, what is the probability of getting 5 green M&Ms in a package, using binomial distribution?

Solution

In a package of M&Ms there are $n = 20$ pieces.

Assuming that the M&M colors occur with equal probability, the probability of getting green M&Ms in a package is $p = \frac{1}{6}$.

The probability of getting 5 green M&Ms in a package is

$$\Pr(X = 5) = \binom{20}{5} \left(\frac{1}{6}\right)^5 \left(1 - \frac{1}{6}\right)^{20 - 5},$$

where

$$\binom{20}{5} = \frac{20!}{(20 - 5)! \cdot 5!} = 15504.$$ $$\Pr(X = 5) = 15504 \left(\frac{1}{6}\right)^5 \left(\frac{5}{6}\right)^{15} = 0.13.$$

Answer: 0.13.

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