Question

Determine the possible ways the following events can occur. Then, determine their probabilities

(a) Rolling a 6 OR a 9

b) Rolling a 3 OR 5 OR 7

c) Rolling an Even AND a multiple of 5

d) Rolling a Multiple of 3 AND a multiple of 4

two, six sided dice are rolled

Answer 1

a)

number of ways to Rolling a 6 OR a 9 =N(rolling a six)+N(rolling a 9)

=5 ways((1,5),(2,4),(3,3),(4,2),(5,1))+4 ways ((3,6),(4,5),(5,4),(6,3))

=9 ways

therefore probability =9/36 =1/4

b)

number of ways to Rolling a 3 OR 5 OR 7 =N(roll 3)+N(roll 5)+N(roll 7) =2+4+6=12

therefore probability =12/36 =1/3

c)

number of ways =Number of ways of rolling 10 =3 ways ((4,6),(5,5),(6,4))

therefore probability =3/36 =1/12

d)

number of ways =Number of ways of rolling 12 =1 ways (6,6)

therefore probability =1/36