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

2 Answers
Oct 15, 2017

1/12112

Explanation:

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

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

Probability of rolling a three color(magenta)AArarr 1/616
Probability of rolling an even number color(blue)BB: you either get a 2,42,4 or 66. rarr 3/636

P(A)*P(B)=1/6*3/6P(A)P(B)=1636
=1/12=112

Oct 17, 2017

color(blue)(2/3)23

Explanation:

We have two events A and B:

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

P(A) = 3/6=1/2P(A)=36=12

P(B)= 1/6P(B)=16

Since this is an A or B event occurring, we have a union of events. i.e. AuuBAB. 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)P(AorB)=P(A)+P(B)12+16=46=23

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)46=23