Question

two dice one grey and one red are thrown at the same time. what is the probability that the sum of the two numbers appearing on the top of the dice is (1) 8 (2) less than or equal to 12​

Answer 1

Given:

2 dice one grey and one red are thrown at same time.

To find:

Probability that the sum of on dice:

1) 8

2) less than or equal to 12.

Solution:

In a standard dice, there are 6 faces.

Total possibilities when 2 dice are thrown are as follows:

{(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) }

There are a total of 36 possibilities.

Formula for probability of an event E is:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

(1) The sum is 8.

The possibilities that the sum of two dice values is 8:

{(2, 6), (3,5), (4,4), (5,3) ,(6,2)}

A total of 5 favorable cases.

$\therefore P(Sum = 8) = \dfrac{5}{36}$

(2) Sum is less than equal to 12.

If we see all the possibilities, we can see that the sum is always lesser than or equal to 12.

Minimum sum = 2

Maximum sum = 36

Total number of favorable cases = 36

Total number of cases = 36

$\therefore P(Sum \le 12) = \dfrac{36}{36} = 1$

Answer 2

Answer:

Is it of maths or English???