8 kids are randomly grouped two teams, an A team with 4 kids and a B...
8 kids are randomly grouped two teams, an A team with 4 kids and a B team with 4 kids. Each grouping is equally likely.What is the probability that Alex ends up on the same team with at least one of his two best friends (Sarah and Kate)?
Show all work. Use Combinations.
Homework Answers
Let us calculate the probability that Alex ends up on the different team that that his best friends (Sarah and Kate)
Let the Alex be in team 1 and Sarah and Kate be in team 2.
Number of ways remaining 5 kids can be selected for remaining 3 positions in team 1( Rest 2 will go to team 2)
= 5C3 = 10
Similarly, if Alex in in team 2 and Sarah and Kate be in team 1, Number of ways = 10
Total number of ways Alex ends up on the different team that that his best friends = 10 + 10 = 20
Number of ways to select 8 kids into a team of size 4 = 8C4 = 70
probability that Alex ends up on the different team that that his best friends (Sarah and Kate) = 20 / 70 = 2/7
probability that Alex ends up on the same team with at least one of his two best friends (Sarah and Kate)
= 1 - probability that Alex ends up on the different team that that his best friends (Sarah and Kate)
= 1 - 2/7
= 5/7
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