A college delegation is made up of 6 basketball players, 5 volleyball players, 4 netball players, 3 badminton players and 2 tennis players. A subcommittee of four people is to be formed from these 20 athletes.
Find the probability that the subcommittee contains exactly one basketball player or exactly one volleyball player (or both).
My method:
let A be the event that committee has one basketball player
let B be event that committee has one volleyball player
so we want P (A U B)= P(A) + P(B) - P (A n B)
(n is intersect)
P(A) = 6C1 x 14C3/20C4
P(B) = 5C1 x 15C3/20C4
P(A n B) = 6C1 x 5C1 x9C2/20C4
my answer is 0.697 but the answer given is 0.414 can someone tell me where i went wrong? thanks~
yes, you take the 3 cases separately: (1) where there is exactly one basketball player and no volleyball player, (2) where there is exactly one volleyball player and no basketball player and (3) where there is exactly one basketball player and exactly one volleyball player, and then you divide the total number of outcomes in these 3 events by the total possible number of outcomes.
Technically though, isn't the method I first used correct? Where I add up P(A) and P(B) and subtract the intersect? Did I make a calculation error? I would've thought I answered the question properly.