Q. 135.0( 2 Votes )

Two different dic

Answer :

Given two different dice are tossed together. The number of possible outcomes are 36:


{1, 1}, {1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 6}, {2, 1}, {2, 2}, {2, 3}, {2, 4}, {2, 5}, {2, 6}, {3, 1}, {3, 2}, {3, 3}, {3, 4}, {3, 5}, {3, 6}, {4, 1}, {4, 2}, {4, 3}, {4, 4}, {4, 5}, {4, 6}, {5, 1}, {5, 2}, {5, 3}, {5, 4}, {5, 5}, {5, 6}, {6, 1}, {6, 2}, {6, 3}, {6, 4}, {6, 5}, {6, 6}


(i) Let E be the event ‘number on each die is even’.


The outcomes favourable to E are {2, 2}, {2, 4}, {2, 6}, {4, 2}, {4, 4}, {4, 6}, {6, 2}, {6, 4} and {6, 6}.


Thus, the number of outcomes favourable to E is 9.


We know that probability of an event E, P (E)


P (E) = 9/36 = 1/4


P (getting a number on each die even) = 1/4


(ii) Let F be the event ‘sum of numbers is 5’.


The outcomes favourable to F are {1, 4}, {2, 3}, {3, 2}, {4, 1}.


Thus, the number of outcomes favourable to F is 4.


P (F) = 4/36 = 1/9


P (sum of numbers is 5) = 1/9


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