# In a Simultaneous Throw of a Pair of Dice, Find the Probability of Getting: a Sum Less than 7 - Mathematics

In a simultaneous throw of a  pair of dice, find the probability of getting:

a sum less than 7

#### Solution

$\text{ When a pair of dice is thrown simultaneously, the sample space will be as follow }:$
$S = \left\{ \left( 1, 1 \right), \left( 1, 2 \right), \left( 1, 3 \right), \left( 1, 4 \right), \cdots\left( 6, 5 \right), \left( 6, 6 \right) \right\}$
$\text{ Hence, the total number of outcomes is 36 } .$

$\text{ Let A be the event of getting pairs whose sum is less than 7 } .$
$\text{ The pairs whose sum is less than 7 are } \left( 1, 1 \right), \left( 1, 2 \right), \left( 1, 3 \right), \left( 1, 4 \right), \left( 1, 5 \right), \left( 2, 1 \right), \left( 2, 2 \right), \left( 2, 3 \right), \left( 2, 4 \right), \left( 3, 1 \right), \left( 3, 2 \right), \left( 3, 3 \right), \left( 4, 1 \right), \left( 4, 2 \right) \text{ and } \left( 5, 1 \right) .$
$\text{ Hence, the number of favourable outcomes is }15 .$
$\therefore P\left( A \right) = \frac{\text{ Number of favourable outcomes }}{\text{ Total number of outcomes }} = \frac{15}{36} = \frac{5}{12}$

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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 26 Data Handling-IV (Probability)
Exercise 26.1 | Q 3.1 | Page 15