Question

A pair of fair dice is cast. What is the probabiliy that at least one of the numbers falling uppermost is a 1

Answer 1

The probability that at least one of the numbers falling uppermost is a 1 is
`(11)/(36)`

Explanation:

If a pair of fair dice, lets say diceA and diceB, is cast:

At least one of the numbers falling uppermost is a 1 can happen in three different ways:

1. both are 1
2. diceA is 1 and diceB is not 1
3. diceA is not 1 and diceB is 1

We should calculate all the 3 probabilities and sum them up.

1)
`(1)/(6) *(1)/(6)` =
`(1)/(36)`

2)
`(1)/(6) *(5)/(6)` =
`(5)/(36)`

3)
`(5)/(6) *(1)/(6)` =
`(5)/(36)`

Then the probability that at least one of the numbers falling uppermost is a 1 is:

`(1)/(36) +(5)/(36) +(5)/(36) =(11)/(36)`