Question

BINOMIAL PROBLEM:

     SUPPOSE that you have 7 SEALED pieces of paper, each one having a different digit from 1 to 7, inclusive.

     NIINE CONSECUTIVE TIMES, AT RANDOM, WITH REPLACEMRENT, you choose a piece of paper

     from your set of 9 pieces of paper.

    Please determine the ( BINOMIAL ) probability that you choose an ODD digit AT LEAST TWICE ?

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 = 4/7 (as there are 4 7s among 7 ) = 0.57142857142

N = number of trials = 9

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)) = 0.99365907985