Question

Two fair dice are rolled. What is the probability that the sum of the numbers rolled is 7?

Answer 1

The probability that the sum of the numbers rolled is 7 is $\frac{1}{6}$

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) }

Total number of possible outcomes = 36

Favorable outcomes = getting sum of the numbers rolled is 7

Favorable outcomes = (1 , 6 ) , (2 , 5 ) , (3 , 4) , (4 , 3) , (5 , 2) , (6 , 1)

Number of favorable outcomes = 6

The probability of an event is given as:

$Probability = \frac{ \text{ number of favorable outcomes }}{ \text{ number of possible outcomes }}\\\\Probability = \frac{6}{36}\\\\Probability = \frac{1}{6}$

Thus probability that the sum of the numbers rolled is 7 is $\frac{1}{6}$