Question

A die is tossed twice. Getting an odd number in at least a toss is termed as a success. Find the probability distribution of number of successes. Also find expected number of success

Answer 1

  Let S be the number of Success events.
  P(S = 1) in one toss = 3/6 = p = 1/2  by getting an odd number
  P(S = 0)  in one toss = 3/6 = 1 - p = 1/2  by getting an even number.

In two tosses:
   P(S = 0) = (1-p) * (1-p) = 1/4
   P(S = 1) = p * (1-p)  +  (1-p) * p = 1/4 + 1/4 = 1/2
   P(S = 2) = p * p = p² = 1/4

$E(S)=\Sigma_{S=0}^{2}\ S * P(S)=0*1/4+1*1/2+2*1/4=1$