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.
Accepted Solution
A:
Answer:Pr(the sum of the numbers rolled is either a multiple of 3 or an even number)=[tex]\frac{2}{3}[/tex]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 | = 36Out of which 11 pairs have the sum multiple of 3 and 18 pairs having sum even.So Pr(A)= [tex]\frac{11}{36}[/tex]and Pr(B)= [tex]\frac{18}{36}[/tex]and Pr(A∩B) = [tex]\frac{5}{36}[/tex], 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) = [tex]\frac{11}{36}[/tex] + [tex]\frac{18}{36}[/tex] - [tex]\frac{5}{36}[/tex] = [tex]\frac{24}{36}[/tex] = [tex]\frac{2}{3}[/tex]