What is the probability of rolling two six-sided dice and obtaining a 6 and a 6?

Solution:

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x.

Given, two six-sided dice are rolled.

The possible outcomes are

(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)

We have to find the probability of obtaining a 6 and a 6.

P = ratio of the number of favorable outcomes to the total number of outcomes of an event

⇒ P = 1/36

This implies the probability of obtaining a 6 on the first die and a 6 on second die.

From the possible outcomes,

P(6 and 6) = 1/36

Therefore, P(6 and 6) = 1/36

What is the probability of rolling two six-sided dice and obtaining a 6 and a 6?

Summary:

The probability of rolling two six-sided dice and obtaining a 6 and a 6 is 1/36.