Question

You roll a number cube twice. What is the probability of rolling an even number and a 5?

Answer 1

`1/6`

Explanation:

P(even)=`1/2`

P(5)=`1/6`

So the probability of `(even nn 5)=1/2xx1/6=1/12`
But you could also get `(5 nn even)1/12`

`1/12+1/12=1/6`

Answer 2

`6/36 = 1/6`

Explanation:

Before we calculate an answer, drawing a possibility space allows us to see all the `36` outcomes of throwing a cube twice.
The grid shows the sum of the two throws.

The red values are those which have a `5` and and an even number

`6|" "7" "8" "9" "10" "color(red)(11)" "12`
`5|" "6" "color(red)(7)" "8" "color(red)(9)" "10" "color(red)(11)`
`4|" "5" "6" "7" "8" "color(red)(9)" "10`
`3|" "4" "5" "6" "7" "8" "9`
`2|" "3" "4" "5" "6" "color(red)(7)" "8`
`1|ul(" "2" "3" "4" "5" "6" "7)`
`color(white)(xxxx)1" "2" "3" "4" "5" "6`

`P(5 and "even") = 6/36 =1/6`

Using a calculation:

`P(5 and "even") = P(5, "even") " OR " P("even", 5)`

`= (1/6 xx 3/6) + (3/6 xx1/6)`

`=3/36 +3/36`

`=6/36`

`=1/6`