Question

A batch of 24 articles consist of 14 good ones, 6 with only minor defects, and 4 with major defects. Two articles are taken at random, tested, and replaced. Use a tree diagram to find the probability that:

a) One article is good while the other has a major defect.
b) One article has a major defect while the other article has a minor defect.

Answer 1

To find the probability of selecting one article that is good and one article with a major defect, we can use a tree diagram. The probability would be 7/72.

Step-by-step explanation:

To find the probability of selecting one article that is good and one article with a major defect, we can use a tree diagram. First, we start with the initial batch of 24 articles. From there, we branch out into three possibilities: selecting a good article and then a major defect article, selecting a minor defect article and then a major defect article, or selecting a major defect article and then a good article. Each branch is labeled with the probability of that outcome. The final probability is the sum of the probabilities of the two branches that represent selecting one good article and one major defect article.

In this case, the probability would be:

Probability = (14/24) * (4/24) + (6/24) * (4/24) = 56/576 = 7/72