Question

Events A and B are disjointed.

P(A) = 8/15 ; P(B) = 4/15

Find P(A or B).

Answer 1

P(A) + P(B)
8/15 + 4/15
12/15
It can be simplified to 4/5

Answer 2

`P(A\hspace{3}or\hspace{3}B)=(4)/(5)=0.8 =80\%`

Explanation:

If Events A and B are disjointed, this means that they are mutually exclusive events. Mutually exclusive events are those that if one event happens means that the other cannot occur. For this type of event the following properties are true:

`A\cap B = \emptyset,\\\\P(A\cup B)=P(A\hspace{3}or\hspace{3}B)=P(A)+P(B)`

Therefore:

`P(A\hspace{3}or\hspace{3}B)=P(A)+P(B)\\\\P(A\hspace{3}or\hspace{3}B)=(8)/(15) +(4)/(15) =(12)/(15) =(4)/(5) =0.8`

You can also write the result as a percentage just multiplying by 100:

`P(A\hspace{3}or\hspace{3}B)=0.8*100=80\%`