Stacy rolls a pair of six-sided fair dice.
the probability that the sum of the numbers rolled is either a multiple of 3 or an even number is
, and the two events are exclusive.

2/3 and NOT mutually exclusive

Step-by-step explanation:

plato

Pr(the sum of the numbers rolled is either a multiple of 3 or an even number)=

Step-by-step explanation:

Let A be the event "sum of numbers is multiple of 3"

and B be the event "sum is an even number".

As our dice has six sides, so the sample space of two dices will be of 36 ordered pairs.

|sample space | = 36

Out of which 11 pairs have the sum multiple of 3 and 18 pairs having sum even.

So Pr(A)=

and Pr(B)=

and Pr(A∩B) = , as 5 pairs are common between A and B.

So now Pr(A or B)= Pr(A∪B)

                            = Pr(A)+Pr(B) - Pr(A∩B)

                            = + -

                            =

                            =

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