Answer :

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 pi and xi.


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


The following table gives probability distribution:



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