Question

find the probability of not getting a sum 7 in a single throw with a pair of dice

Answer 1

$\huge{\mathcal{\underline{\green{SOLUTION}}}}$

A pair of dice is rolled once

So the total number of possible outcomes

$= {6}^{2} = 36$

Let A be the event that of getting a sum of 7

Then the points of the event A is

$(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)$

So the total number of possible outcomes for the event A is 6

So the probability for the event A is P(A)

$= \frac{6}{36} = \frac{1}{6}$

So the required probability

$= P( {A}^{c} ) \: = 1 - \: P(A) = 1 - \frac{1}{6} = \frac{5}{6}$