Question

What is the probability all 6 faces of a fair die turn up at least twice in 20 rolls.

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 = 1/6 = 0.167

N = number of trials = 20

R = desired success = at least 2

We know that sum of all the probabilities is = 1.

So, P(at least 2) = 1 - (p(0) + p(1)) = 0.87037062968