Two six-sided dice are rolled. A. Mathematically show (using the intersection de

Question

Two six-sided dice are rolled.

A. Mathematically show (using the intersection definition) the probability of throwing a 3 on a die one and a 4 on die two. Use a Venn diagram for guidance.

B. Based on throwing both dice twice, mathematically show (using the union definition) the probability of throwing:

- a 7 on the first roll or double ones on the second

- a 7 on the first roll or second roll

- a 7 on the first roll or any doubles on the second roll

C. Two dice are rolled and the sum of the numbers is even. What is the probability that the sum is greater than 8? (Using the conditional probability definition)

Explanation / Answer

answer

A) here sample space S=

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

n(s)=36

A= the probability of throwing a 3 on a die one and a 4 on die two.

=(3,4)

n(A)=1

P(A)=n(A)/n(S)=1/36

B)All event has no any element,this is impossible events

C)

C=Two dice are rolled and the sum of the numbers is even

n(C)=18

D=the probability that the sum is greater than 8

n(D)=4

=P(C intersection D)/P(D)

=1

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.