The game of Befuddled involves rolling a balanced sevensided

The game of Befuddled involves rolling a balanced, seven-sided die marked with the numbers, 1,2,3,4,5,6, and 7. Suppose the die is rolled six times in succession. Calculate the probability that the six rolls will result in exactly two 3\'s by using the binomial formula.

Report your answer to FOUR decimal places

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( Probability getting numkber two) = 1/7 = 0.1429

P( X = 2 ) = ( 6 2 ) * ( 0.1429^2) * ( 1 - 0.1429 )^4
= 0.1653