In the toss of 5 dice what is the probability of obtaining 2

In the toss of 5 dice what is the probability of obtaining 2 or fewer ones? Explain

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 throwing a dice getting any number = 1/6 = 0.1667
P( X = 2 ) = ( 5 2 ) * ( 0.1667^2) * ( 1 - 0.1667 )^3
= 0.161

P( X = 1 ) = ( 5 1 ) * ( 0.1667^1) * ( 1 - 0.1667 )^4
= 0.402

P(toss of 5 dice what is the probability of obtaining 2 or fewer ones) = P( X = 2 ) + P( X = 1 ) = 0.161 + 0.402 = 0.503