A fair dice is tossed twice.

Every time a throwing dice is an independent event.

Note: P(AՈB) = P(A)P(B) where A and B are independent events.

Let A denote the event of getting a number less than 3 on a single throw of dice.

∴ P(A) = {out of 6 outcomes 1 and 2 are favourable}

P(not A) = P(A’) =

As success is considered when number appearing on dice is less than 3.

Let X denotes the success.

As we are throwing two dice so that we can get success in both throws or either one of them, or we may even not get succeed.

∴ X can take values 0,1 or 2

P(X = 0) = P(not success)× P(not success) = P(A’)× P(A’) =

P(X = 1) = P(A) ×P(A’)+ P(A’)×P(A)

=

P(X = 2) = P(success)× P(success) = P(A)× P(A) =

Now we have p_i and x_i.

∴ Now we are ready to write the probability distribution for X:-

The following table gives probability distribution: