A cricket eleven is to be selected out of a group of 14 players.

Question

A cricket eleven is to be selected out of a group of 14 players. The
probability that the team includes at least one of two specified players
A and B is??

Answer 1

You can solve this by picking all combinations of 11 where at least one of A & B get to play divided by all combinations of 11 player combos (this is also known as a hypergeometric distribution).

 

P(1 of A&B gets picked) =

2C1 * 12C10 / 14C11  

(this saying all combos where 1 of A&B gets picked * all combos where 10 of the remaining 12 players gets picked, divided by all combos of 11 player teams)

=(2 * 6 * 11 )/ (14*13*2)

= 33/91

 

P(both A & B get picked) =

2C2 * 12C9 / 14C11

= (1 * 2 * 10 * 11) / (14 * 13 * 2)

= 55/91

 

P(at least 1 of A or B gets picked) = 33/91 + 55/91 = 88/91 = 96.7%

 

We can double check this by trying out P(neither gets picked), since that should be 3/91 since it is the only other possible outcome.

 

P(neither gets picked) = 

2C0 * 12C11 / 14C11

12 / (14*13*2)

3/91

 

So it checks out and the answer is 96.7%.