A particularly intense peewee basketball coach decides to place his players into

Question

A particularly intense peewee basketball coach decides to place his players into groups based on theirskills.Theteamconsistsof12playersofwhichthecoachclassies4asthree-pointspecialists, 6asdefensivestandouts, and5asneitherthree-pointspecialistsnordefensivestandouts.Aplayeris chosen at random. Let T denote the event that a three-point specialist is selected and D denote the event that a defensive standout is selected. Find the probability of the following events. a The selected player is a three-point specialist and a defensive standout. b The selected player is a defensive standout but not a three-point specialist. c The selected player is either a three-point specialist or a defensive standout.

Explanation / Answer

A player can be a three-point specialist or defensive standout or both or none. Out of 12, 5 are neither defensive standouts nor three-point specialists. So, Out of remaining 12, let a be only defensive standouts and b be only three-point specialists. So, 7-a-b are both

Hence, a+7-a-b=6, b=1

b+7-a-b=4, a=3

a. P(both) = (7-a-b)/12 = 3/12 = 0.25

b. P(only defensive standout) = a/12 = 3/12 = 0.25

c. P(either 3 point specialist or defensive standout) = (12-5)/12 = 7/12

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