Question

Simon is rolling two fair dice. He thinks the probability of getting two sixes is `1/36`. Is this correct and why or why not?

Answer 1

`"correct"`

Explanation:

`"the probability of obtaining a 6 is"`

`P(6)=1/6`

`"to obtain the probability of getting 2 sixes multiply the"`
`"probability of each outcome"`

`"6 AND 6 " =1/6xx1/6=1/36`

Answer 2

`1/36` is correct

Explanation:

There are 6 different outcomes on each die. Each outcome on one die can be combined with each outcome on the other.

This means there are `6xx6=36` different possibilities.

However, there is only one way of getting two sixes.

So the probability of double `6` is `color(red)(1/36)`

This is shown in the table below.

`color(blue)(" "1" "2" "3" "4" "5" "6)`

`color(blue)(1):" "2" "3" "4" "5" "6" "7`

`color(blue)(2):" "3" "4" "5" "6" "7" "8`

`color(blue)(3):" "4" "5" "6" "7" "8" "9`

`color(blue)(4):" "5" "6" "7" "8" "9" "10`

`color(blue)(5):" "6" "7" "8" "9" "10" "11`

`color(blue)(6):" "7" "8" "9" "10" "11" "color(red)(12)`

Answer 3

He is correct.

Explanation:

Let's look at just one die for now. The probability for getting a `6` on one die is `1/6` since there are `6` sides to a die, each number from `1` to `6` occupying a side. The other die is also the same, with numbers `1` to `6` occupying one side of the die. This also means that the probability of rolling a `6` on the second die is also `1/6`. Combined, the probability that you roll a `6` on both dies is

`1/6*1/6=1/36`

This means that Simon is correct.