Question

a pair of dice id thrown once.find the probability of getting (1)same number on both dice(2)a total of 9(3) an even prime number as sum

Answer 1

Answer :

The following outcomes will be got when we throw two dices at once.

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

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

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

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

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

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

Probability = Number of favourable outcome / Total number of outcome

1. Same number on both side -

Probability = Number of favourable outcome / Total number of outcome

⇒ $\sf\frac{6}{36}$

⇒ $\sf\frac{1}{6}$

2. A total of 9 -

Probability = Number of favourable outcome / Total number of outcome

⇒ $\sf\frac{4}{36}$

⇒ $\sf\frac{1}{9}$

3. An even prime number as sum -

Probability = Number of favourable outcome / Total number of outcome

⇒ $\sf\frac{1}{36}$

Answer 2

Answer:

A pair of dice is thrown once.

So, two dices are thrown once

Number of outcomes on throwing one dice = 6

⇒ Total number of outcomes = 6² = 36

(1) Same number on both dice :

The possible outcomes for this are : (1, 1) , (2, 2) , (3, 3) , (4, 4) , (5, 5) , (6, 6)

Number of possible outcomes = 6

Hence, The probability = 6/36

                                        = 1/6

(2) A total of 9

The possible outcomes for this are : (3, 6) , (4, 5) , (6, 3) , (5, 4)

Number of possible outcomes = 4

Hence, The probability = 4/36

                                        = 1/9

(2) An even prime number as a sum

The possible outcomes for this are : (1, 1)

Number of possible outcomes = 1

Hence, The probability = 1/36