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Question

Mathematics Question on Conditional Probability

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

A

12\frac{1}{2}

B

13\frac{1}{3}

C

14\frac{1}{4}

D

16\frac{1}{6}

Answer

13\frac{1}{3}

Explanation

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 = n(E)n(S) = 1236 =13\frac{n(E)}{n(S)} \, = \, \frac{12}{36} \, =\frac{1}{3}