Answer to Question #164834 in Statistics and Probability for Vasu

Question

A magic bag contains of 10 good articles, 4 with minor defects and 2 with major

defects. Two articles are chosen from the magic bag at random. Find the

probability [5]

(a) Exactly 1 is good

(b) Neither is good

(c) Both has major defects

Answer 1

1. There are two places, where 10 appropriate variants for the first place and 6 for the second, so 10 * 6 = 60 all variants. It's necessary to divide by all possible variants - 16*15/2 (16 variants on the first place and 15 on the second, because one article is occupied on the first place, after that divide by 2 because the order is not important). The probability is equal to (10*6)/(16*15/2) = 1/2
2. There are 16-10 = 6 articles, which have minor or major defects. So we have 6*5 = 30 variants to choose "minor or major" articles and 16*15/2 = 150 all variants. The probability is equal to (6*5)/(16*15/2) = 1/4
3. Obviously, there is only one appropriate variant to choose two "major" articles. And also 150 all possible variants. The probability is equal to 1/150