Question

Among 10 laptop computers, five are good and five have defects. Unaware of this, a customer buys 6 laptops. How many of the laptops purchased by the customer are likely to have defects?

1) 0
2) 1
3) 2
4) 3
5) 4
6) 5
7) 6

Answer 1

To find the likely number of defective laptops purchased, we would calculate the probability for each potential outcome (0 to 6 defects) using the hypergeometric distribution and then identify which has the highest probability.

The correct answer is 7).

Step-by-step explanation:

The question asks to determine the likely number of defective laptops purchased by a customer who buys 6 laptops from a batch of 10 where five are good and five have defects. We need to calculate the probability of getting a certain number of defects in the 6 laptops the customer buys. This problem involves concepts of combinatorics and probability.

We can use the hypergeometric distribution to solve this problem because the selection is without replacement. To find the probability of getting x defective laptops, we can use the formula:

P(X = x) = (combinations of defective laptops) * (combinations of non-defective laptops) / (total combinations of 6 laptops)

We calculate this for each number of defective laptops the customer could receive (0 through 6). The most likely number of defective laptops will have the highest probability. This is a complex calculation, and a graphing calculator or statistical software could be used to expedite the process.