I play in a hand bell choir at my church We have ten positio

I play in a hand bell choir at my church. We have ten positions (hand bell players) in the choir. There are five women and five men. For our ten hand bell members, all of the hand bell choir members drive to rehearsal in their own cars or trucks. One member drives a black Dodge Ram. An interesting note, though, is that two of the hand bell choir members drive a red Toyota Prius to rehearsal (not just a red Toyota, but a red Toyota Prius). Determine the probability of having two hand bell choir members driving a red Toyota Prius (matching colors) to rehearsal. State any assumptions you use to solve this problem.

Solution

Out of 10 people, 2 people already drive in a red toyota prius and 1 person drives a black dodge ram.

It is unknown what the rest 7 people drive, we have to add here that some or all or none of them may also drive a red toyota prius.

Using bayes law,

assuming only 2 red toyota prius,

numerator (choose any 2 out of 10 for the red toyota prius and choose 1 out of remaining 8 for the black dodge ram) = 10C2*8C1=45*8=360

denominator (2 or more than 2 can be red toyota prius) = (10C2*8C1)+(10C3*7C1)+(10C4*6C1)+(10C5*5C1)+(10C6*4C1)+(10C7*3C1)+(10C8*2C1)+(10C9*1C1) = 360+840+1260+1260+840+360+90+10=5020

Hence required prob = 360/5020 = 18/251