Question

Suppose that 60% of all computers sold by a large computer retailer are laptops and 40% are desktop models. The types of computers purchased by each of the next 12 customers will be recorded. Define a random variable x as x = number of laptops among these twelve. What is the probability that exactly four are purchased laptops amongst these 12?

Answer 1

The random variable X represents the number of laptops among the twelve customers. To find the probability that exactly four laptops are purchased, we can use the binomial probability formula.

Step-by-step explanation:

a. The random variable X represents the number of laptops among the twelve customers.

b. To find the probability that exactly four laptops are purchased, we can use the binomial probability formula. The probability of purchasing a laptop is 0.6, and the probability of not purchasing a laptop is 0.4. The formula is P(X=k) = (nCk) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, p is the probability of success, and (nCk) is the number of combinations. Here, n = 12, k = 4, p = 0.6, and (nCk) = 12C4, which can be calculated as 495. Therefore, the probability that exactly four laptops are purchased is P(X=4) = 495 * (0.6)^4 * (0.4)^(12-4).