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

#1/12#

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#

Oct 17, 2017

#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)#