Question

Roll two fair dice separately. Each die has six faces. a. List the sample space. b. Let A be the event that either a three or four is rolled first, followed by an even number. Find P(A). c. Let B be the event that the sum of the two rolls is at most seven. Find P(B). d. In words, explain what "P(A|B)" represents. Find P(A|B). e. Are A and B mutually exclusive events? Explain your answer in one to three complete sentences, including numerical justification. f. Are A and B independent events? Explain your answer in one to three complete sentences, including numerical justification.

Answer 1

Answer:

Step-by-step explanation:

a) {(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)}

$\Omega$=6*6=36

b)A=(2*3)=6

P(A)=6/36=1/6

c) B=6+5+4+3+2+1=21

P(B)=21/36

d) P(A|B) - an event where either a 3 or 4 is rolled first and is followed by an even number and their sum goes over 7

P(A|B)=3

e) Not always, not sure how to explain, I'm not good with English Math

f) Same as above