Question

A lot of 10 components contains 4 that are defective. Two components are drawn at random and tested. What is the probability that both components are defective?

1) 1/45
2) 1/36
3) 1/20
4) 1/10

Answer 1

The probability that both components drawn are defective is 1/30.

Step-by-step explanation:

To find the probability that both components drawn are defective, we need to use the concept of probability with replacement. Since there are 4 defective components out of 10 total, the probability of drawing a defective component on the first draw is 4/10. After the first draw, there will be 9 components left, 3 of which are defective. So, the probability of drawing a defective component on the second draw is 3/9.

To find the probability of both events happening, we multiply the individual probabilities: (4/10) * (3/9) = 12/90 = 1/7.5 = 1/30.

Therefore, the probability that both components drawn are defective is 1/30, which is not listed among the given answer choices.