Question

A warehouse contains ten printing machines, four of which are defective. A company selects five of the machines at random, thinking all are in working condition. What is the probability that all five of the machines are nondefective?

Answer 1

The probability that all five randomly selected machines from a warehouse containing ten machines, four of which are defective, are nondefective is \(\frac{1}{42}\) or approximately 0.0238.

Step-by-step explanation:

To determine the probability that all five of the machines selected from the warehouse are nondefective, we can use combinatorics, specifically the hypergeometric distribution. The total number of ways to select five machines from the ten available is the combination of 10 taken 5 at a time, denoted as C(10,5). Out of these ten machines, we have six that are nondefective. So, the number of ways to select five nondefective machines out of the six available is C(6,5). Therefore, the probability is the number of successful outcomes over the number of total possible outcomes, which can be mathematically represented as:

P(all five are nondefective) = \(rac{C(6,5)}{C(10,5)}\)

Calculation:

• C(6,5) = 6 (since there are six ways to choose five out of six)
• C(10,5) = 252 (the number of ways to choose five out of ten)

Thus:

P(all five are nondefective) = \(rac{6}{252}\) = \(rac{1}{42}\)

The probability that all five randomly selected machines are nondefective is \(\frac{1}{42}\) or approximately 0.0238.