Question

Stacy rolls a pair of six-sided fair dice.

Answer 1

Answer:

Pr(the sum of the numbers rolled is either a multiple of 3 or an even number)=$\frac{2}{3}$

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)= $\frac{11}{36}$

and Pr(B)= $\frac{18}{36}$

and Pr(A∩B) = $\frac{5}{36}$, 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)

                            = $\frac{11}{36}$ + $\frac{18}{36}$ - $\frac{5}{36}$

                            = $\frac{24}{36}$

                            = $\frac{2}{3}$