Question

When rolling a pair of die, how likely is it you will get a sum of 3 or 4?

		5.6%
		8.3%
		13.9%
		16.7%

When rolling a pair of die, how likely is it you will not get doubles?

		8.3%
		16.7%
		83.3%
		91.7%

When rolling a pair of die, how likely is it you will get an odd number and a number less than 8?

	A.	27.8%
	B.	33.3%
	C.	38.9%
	D.	75%

When rolling a pair of die, how likely is it you will get an odd number or a number less than 8?

	A.	33.3%
	B.	75%
	C.	83.3%
	D.	108.3%

Answer 1

When rolling a dice total outcomes in sample space=36

(a) Let E is the event having sum 3 or 4, such that

E={(1,2),(2,1),(3,1),(1,3),(2,2)}, then

P(E)=5/36=0.138888889=13.9%

(b) E={(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)}, then

P(not getting doubles)=1-P(E)=1-6/36=0.83333=83.3%

(c) E={(1,2),(2,1),(1,4),(4,1),(3,2),(2,3),(1,6),(6,1),(2,5),(5,2),(3,4),(4,3)}

P(E)= 12/36=0.3333=33.3&%

(d) Let A be the event getting odd numer and B is the event getting a number less than 8, then

P(A)=30/60=1/2

B={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(5,1),(5,2),(6,1)}

n(B)=21

(A disjoint B)= {(1,2),(1,4),(1,6),(2,1),(2,3),(2,5),(3,2),(3,4),(4,1),(4,3),(5,2),(6,1)}

n(A disjoint B)= 12

P(A or B)= P(A)+P(B)-P(A disjoint B)=1/2+21/36-12/36=0.75=75%