Need all answers, thanks for the help in advance! EXERCISE 4 Roll two fair dice.

Question

Need all answers, thanks for the help in advance!

EXERCISE 4 Roll two fair dice. Each die has 6 faces. b. Let A be the event that either a 3 or 4 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 7. Find P(B) d. In words, explain what "P(A B)" represents. Find P(AB) e. Are A and B mutually exclusive events? Explain your answer in 1- 3 complete sentences, indluding numerical justification. f. Are A and B independent events? Explain your answer in 1- 3 complete sentences, including numerical justification Find (a) P(A and B) (c) P(A B) (b) P(A or B) (d) P(B | A)

Explanation / Answer

b)sample space of A ={(3.2).(3.4),(3,6),(4,2),(4,4),(4,6)}

here P(A) =6/36 =1/6 ( 6 favourable events out of 36)

c)sample space of 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)}

P(B)=21/36 =7/12

d)P(A|B) represent probability of happening of event A given event B happened.

P(A|B) =3/21 =1/7 (as there are 3 events of B where A happens ={)3,2),(3,4),(4,2)}

e) No. as for mutually exclusive they must not share common subsets . or P(A|B) should be equal to 0.

f)No as for that probability of A should be indifferent given B ; or P(A|B) should be equal to P(A)

a)P(A and B) =3/36 =1/12 ( there are 3 common elements)

c) P(A or B) =24/36 =2/3 ( there are ttotal 24 elements in which A or B can happen)

b)P(A|Bc) =3/15 =1/5 ( there are 3 elements which are common b/w A and Bc out of 15 elements of Bc)

d)P(B|A) =3/6 =1/2 ( there are 3 common elements in A and B out of 6 elements oif B)

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