Question

Suppose that two fair dice are rolled. Find the probability that the number on the first die is a 6 or the number on the second die is a 4.

Answer 1

`Probability = (1)/(36)`

Explanation:

Given

Two fair dice

Required

Determine the probability that the outcomes is 6 on the first and 4 on the second

First, we need to write out the sample space of both:

`S_1 = \{1,2,3,4,5,6\}`

`n(S_1) = 6`

`S_2 = \{1,2,3,4,5,6\}`

`n(S_2) = 6`

Where S1 represents the first and S2, the second

The probability of outcome of 6 on the first is:

`P(6) = (n(6))/(n(S_1))`

`P(6) = (1)/(6)`

The probability of outcome of 4 on the second is:

`P(4) = (n(4))/(n(S_2))`

`P(4) = (1)/(6)`

So, the required probability is then calculated as:

`Probability = P(6) * P(4)`

`Probability = (1)/(6) *(1)/(6)`

`Probability = (1)/(36)`