A die is a numbered in such a way that its face show the numbers 1, 2, 2, 3, 3, 6. It is thrown two times and the total score in two throws is noted. Complete the following table which gives a few values of the total score on the two throws :

What is the probability that the total scene is (i) even, (ii) 6, (iii) at least 6.

Solution

Number of possible outcomes = 36
i.e. n(S) = 36
(i) Let A be the favourable outcomes that the total score is even. Then n(A) = 18
Therefore, P(A) = $fraction numerator straight n left parenthesis straight A right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 18 over 36 equals 1 half.$

(ii) Let B be favourable outcomes that the total score is 6. Then
n(B) = 4
Therefore. P(B) = $fraction numerator straight n left parenthesis straight B right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 4 over 36 equals 1 over 9.$
(iii) Let C be the favourable outcomes that total score is at least 6. Then n(C) = 15
Therefore, P(C) = $fraction numerator n left parenthesis C right parenthesis over denominator n left parenthesis S right parenthesis end fraction equals 15 over 36 equals 5 over 12$ .

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