Question

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.

Answer 1

2/3 and NOT mutually exclusive

Explanation:

plato

Answer 2

Pr(the sum of the numbers rolled is either a multiple of 3 or an even number)=
`(2)/(3)`

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)=
`(11)/(36)`

and Pr(B)=
`(18)/(36)`

and Pr(A∩B) =
`(5)/(36)`, 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)

=
`(11)/(36)` +
`(18)/(36)` -
`(5)/(36)`

=
`(24)/(36)`

=
`(2)/(3)`