3 Binomial distribution Please use Binomial distribution to

3. Binomial distribution: Please use Binomial distribution to compute the probability of obtaining at least one \'\'Six\'\' in rolling a fair die 4 times.

Solution

the possible out comes in throwing of a die are 1,2,3,4,5, and 6.

Probability of getting a six in one throw (p) = 1/6

not getting six (q) = 1- (1/6) = 5/6

a die is throwed four times. the probability of success ( getting a six) in each trail is same = 1/6

n = 4; X is the number of success ( at least one six) = >=1

P(X>=1) = 1- P(X=0) = 1- (4C0) (5/6)^4 =1- 0.4822 = 0.5177