Question

In a single roll of a six-sided dice, what is the probability of rolling a three or an even number?

Answer 1

`1/12`

Explanation:

You have 2 events: A & B.
`color(magenta)A`: rolling a three
`color(blue)B`: rolling an even number

`rArr P(A and B)=P(A)*P(B)`

Probability of rolling a three `color(magenta)A` `rarr 1/6`
Probability of rolling an even number `color(blue)B`: you either get a `2,4` or `6`. `rarr 3/6`

`P(A)*P(B)=1/6*3/6`
`=1/12`

Answer 2

`color(blue)(2/3)`

Explanation:

We have two events A and B:

A being an even number 2 4 6.
B being a 3.

`P(A) = 3/6=1/2`

`P(B)= 1/6`

Since this is an A or B event occurring, we have a union of events. i.e. `AuuB`. This strictly means A or B or both. In this particular case A and B cannot occur simultaneously since they are mutually exclusive events. You can't throw a 3 and an even number, since 3 is an odd number.

So we have:

`P(A or B) = P(A) + P(B)=> 1/2+1/6= 4/6 =color(blue)(2/3)`

We could have obtained this result directly by considering the 2 events as one event:

An even number and 3 is four favourable outcomes, so:

`4/6=color(blue)(2/3)`