A die is thrown three times. Let X be ‘the number of twos seen’. Find the expectation of X.

Question

Philoid · Accepted Answer

Given that, X= no. of twos seen

So, on throwing a die three times, we will have X=0,1,2,3

P(X=1) = P_{not 2.} P_{not 2}. P_{2 +} P _2. P_2. P_{not 2} + P ₂. P_{not 2.} P ₂

P(X=2) =P_{not 2.} P_2. P_{2 +} P_{not 2.} P_2. P_{2 +} P₂. P_{not 2}.P₂

We know that,