Question

In a single throw of a pair of dice, the probability of getting the sum a perfect square is

Options

• \[\frac{1}{18}\]

• \[\frac{7}{36}\]

• \[\frac{1}{6}\]

• \[\frac{2}{9}\]

Answer 1

 A pair of dice is thrown 

TO FIND: Probability of getting the sum a perfect square

Let us first write the all possible events that can occur

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

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

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

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

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

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

Hence total number of events is  `6^2=36`

Favorable events i.e. getting the sum as a perfect square are

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

Hence total number of favorable events is 7

`"We know that PROBABILITY" =  "Number of favourable event"/"Total number of event"`

Hence probability of getting the sum a perfect square is `7/36`