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  4. In rolling two fair dice, what is the probability of obtaining a sum greater than 3 but not exceeding 6 ?

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Q. In rolling two fair dice, what is the probability of obtaining a sum greater than 3 but not exceeding 6 ?

VITEEEVITEEE 2006

Solution:

Let S be the sample space
$\therefore $ n(S) 36
Events
[sum greater than 3 but not exceeding 6]
= {(2, 2), (3, 1), (1, 3), (4, 1), (1, 4), (5, 1) (1, 5),
(3, 2), (2, 3), (4, 2), (2,4), (3, 3)}
$\Rightarrow $ n(E) 12
$\therefore \, \, $ Required probability = $\frac{n(E)}{n(S)} \, = \, \frac{12}{36} \, =\frac{1}{3}$