Question

10 kids are randomly grouped into an A team with five kids and a B team with five kids. Each grouping is equally likely. There are three kids in the group, Alex and his two best friends Jose and Carl. What is the probability that Alex ends up on the same team with at least one of his two best friends?

Answer 1

The probability that Alex ends up on the same team with at least one of his two best friends = 0.7222

Explanation:

Number of ways to select r items from n, nCr = n!/(r! x (n-r)!)

P(Alex ends up on the same team with at least one of his two best friends) = 1 - P(Alex ends upon a team with none of his two best friends)

= 1 - P(4 other people in Alex's group are chosen from the 7 other kids)

= 1 - Number of ways to pick 4 kids from 7 / Number of ways to pick 4 kids from 9

= 1 - 7C4 / 9C4 = 1 - 35/126

= 0.7222