Question

Two fair dice are rolled simultaneously the probability of getting the sum of 3 is give the answer

Answer 1

Total number of outcomes=36

Favourable outcomes= (1,2) ,(2,1)

P(E) = 2/36 =1/18

Answer 2

The probability of getting the sum of 3 is $\frac{1}{18}$

Solution:

When two dice are rolled, sample space is given as:

(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)

Therefore,

Total number of possible outcomes = 36

Favorable outcomes = getting the sum of 3

Favorable outcomes = ( 1 , 2 ) , (2 , 1)

Number of favorable outcome = 2

The probability of an event is given as:

$Probability = \frac{ \text{ number of favorable outcomes }}{ \text{ number of possible outcomes }}\\\\Probability = \frac{2}{36}\\\\Probability = \frac{1}{18}$

Thus the probability of getting the sum of 3 is $\frac{1}{18}$

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