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Question

In a simultaneous throw of a pair of dice, if the probability of getting a sum less then 6 is 5a. Find a.

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Solution

Let S= Total outcomes

E= Favourable outcomes (sum less than 6)

S={(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)}

n(S)=36

E={(1,1) (1,2) (1,3) (1,4) (2,1) (2,2) (2,3) (3,1) (3,2) (4,1)}

n(E)=5

P(E)=n(E)n(S)=1036=518

i.e probability of getting a sum less than 6 is 518=5a

a=18

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