Find the probability that........?

Question

Six stand-up comics, A, B, C, D, E, and F, are to perform on a single evening at a comedy club. The order of performance is determined by random selection. Find the probability that:

 

a. Comic D will perform fifth.

b. Comic A will perform fifth and Comic C will perform fourth.
c. The comedians will perform in the following order:D, A, C, E, B, F.
d. Comic B or Comic F will perform third.

 

(type a simplified fraction)

Answer 1

a. Comic D will perform fifth.

 

This is the same as the probability that he performs in any slot, which is 1/6.

b. Comic A will perform fifth and Comic C will perform fourth.

 

P(A goes 1st) = 1/6

P(C goes 4th | A went 1st) = 1/5

 

So 1/6 * 1/5 = 1/30.

c. The comedians will perform in the following order:D, A, C, E, B, F.

 

You need to figure out the total number of orders first.  That is simply 6! = 720.

 

So the odds of that one specific order is 1/(total orders) =  1/720.

d. Comic B or Comic F will perform third.

 

This is the same as question A, except there are two possibilities for the slot instead of 1. So the answer is 2 * 1/6 = 1/3.