Question

Comp-U-Comp has two computer salepeople working today. Miyuki and Tara. Throughout the day, a total of twenty customers come in and randomly choose which saleperson to speak with regarding the purchase of a new computer. Determine the probability that exatciy ten customers decide to deal with Miyuki.

Answer 1

The question from a student regarding the probability of ten customers choosing Miyuki is addressed using binomial distribution, which is part of high school level mathematics.

Step-by-step explanation:

The probability question presented involves a binomial distribution, which is part of probability theory in mathematics. There are 20 independent chances (customers), each with a 50% probability of choosing Miyuki (since there are two salespeople and the choice is random). The question asks for the probability of exactly ten customers choosing Miyuki, which can be represented by P(X = 10) where X is a binomial random variable.

To calculate this, one would use the binomial probability formula:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
where C(n, k) is the combination of n items taken k at a time, p is the probability of success on a single trial, and n is the total number of trials. In this case, n = 20, k = 10, and p = 0.5. Using this formula, we calculate the probability that exactly ten customers choose Miyuki.