August 12th 2015 was a major historical date in major league

August 12th, 2015 was a major historical date in major league baseball. There are 30 major league baseball teams. On August 12th, all 15 home teams won their games; it is the first time this has happened in major league baseball history. Assuming each team involved has a 50% chance of winning its game, what is the probability that all 15 home teams won their games?

(a) 0.50

(b) 0.0333

(c) 0.0000305

(d) 0.0667

(e) None of the above

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

P( X = 15 ) = ( 15 15 ) * ( 0.5^15) * ( 1 - 0.5 )^0
= 0.0000305