Question

The Mars company says, that before the introduction of purple, yellow made up 20% of their plain M&M candies, red made up another 20%, and orange, blue, and green each made up 10%. The rest were brown. Assuming you had an infinite supply of M&M's with the older color distribution, if you picked six M&M's in a row, what is the probability that at least one is brown?

Do not round intermediate calculations. Round your final answer to four decimals.

Answer 1

First we compute the probability of getting a brown M&M as:
P( brown ) = 1 - P(red) - P(yellow) - P(orange) - P(blue) - P(green) = 1 - 0.2 - 0.2 - 0.1 - 0.1 - 0.1 = 0.3

Given that we have an infinite number of M&Ms with the old probability distribution.

Probability that at least one is brown in the 6 M&Ms picked is computed here as:
= 1 - Probability that none of them is a brown

= 1 - (1 - 0.3)6

= 1 - 0.76

= 0.882351

Therefore 0.8824 is the required probability here.