Question

A 10 sided die with sides numbered 0 through 9 is rolled 5 times. Let X be the number of zeros rolled.
(a) Find the probability that exactly 2 zeros are rolled.
(b) Find the probability that no less than 4 zeros are rolled.
(c) Find the mean and the variance of X.

Answer 1

Answer)

As there are fixed number of trials and probability of each and every trial is same and independent of each other

Here we need to use the binomial formula

P(r) = ncr*(p^r)*(1-p)^n-r

Ncr = n!/(r!*(n-r)!)

N! = N*n-1*n-2*n-3*n-4*n-5........till 1

For example 5! = 5*4*3*2*1

Special case is 0! = 1

P = probability of single trial = 1/10 = 0.1

N = number of trials = 5

R = desired success

A)

P(2) = 5c2*(0.1^2)*(1-0.1)^5-2 = 0.0729

B)

P(4) + P(5)

= 0.00046

C)

Mean = n*p = 5*0.1 = 0.5

Variance = n*p*(1-p) = 5*0.1*0.9 = 0.45