Question

According to the Mars company, packages of milk chocolate M&Ms contain 20% orange candies. Find

the probability that in a random sample of 100 M&M candies, there are 25% or less orange candies and find the probability that there are 25% or more candies

Answer 1

Answer: The problem involves a binomial distribution with n = 100 candies and p = 0.2 probability of success (getting an orange candy).

To find the probability that there are 25% or less orange candies, we need to calculate the cumulative probability of getting 0 to 25 orange candies out of 100:

P(X ≤ 25) = Σ P(X = k), where k goes from 0 to 25

Using the binomial probability formula, we get:

P(X = k) = (100 choose k) * 0.2^k * 0.8^(100-k)

So, the probability of getting 25% or less orange candies is:

P(X ≤ 25) = Σ (100 choose k) * 0.2^k * 0.8^(100-k), where k goes from 0 to 25

Using a calculator or software, we can compute this probability to be approximately 0.058.

To find the probability that there are 25% or more orange candies, we need to calculate the cumulative probability of getting 25 to 100 orange candies out of 100:

P(X ≥ 25) = Σ P(X = k), where k goes from 25 to 100

Using the same binomial probability formula, we get:

P(X = k) = (100 choose k) * 0.2^k * 0.8^(100-k)

So, the probability of getting 25% or more orange candies is:

P(X ≥ 25) = Σ (100 choose k) * 0.2^k * 0.8^(100-k), where k goes from 25 to 100

Using a calculator or software, we can compute this probability to be approximately 0.982.

Therefore, the probability of getting 25% or less orange candies is 0.058 and the probability of getting 25% or more orange candies is 0.982

Explanation: