The probability of a fair coin landing on tails is 50 The fa

The probability of a fair coin landing on tails is 50%. The fair coin is flipped twice. What is the probability that the first AND 2^nd flips are both heads?   Show work.

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

probability of a fair coin landing on tails is 50%
probability of a fair coin landing on head = 100 - 50 = 50%
P( X = 2 ) = ( 2 2 ) * ( 0.5^2) * ( 1 - 0.5 )^0
= 0.25