# In a Simultaneous Throw of a Pair of Dice, Find the Probability of Getting:(Xi) a Sum More than 7 - Mathematics

In a simultaneous throw of a pair of dice, find the probability of getting a sum more than 7

#### Solution

We know that in a single throw of two dices, the total number of possible outcomes is (6 × 6) = 36.
Let S be the sample space.
Then n(S) = 36

Let E11 = event of getting a sum greater than 7
Then E11 = {(2, 6), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6), (5, 3), (5, 4), (5, 5), (5, 6), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
i.e. (E11) = 15

$\therefore P\left( E_{11} \right) = \frac{n\left( E_{11} \right)}{n\left( S \right)} = \frac{15}{36} = \frac{5}{12}$

Concept: Probability - Probability of 'Not', 'And' and 'Or' Events
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 33 Probability
Exercise 33.3 | Q 2.11 | Page 45