Question

You roll two six-sided fair dice. a. Let A be the event that the first die is even and the second is a 2, 3, 4 or 5. P(A) = Round your answer to four decimal places. b. Let B be the event that the sum of the two dice is a 7. P(B) = Round your answer to four decimal places. c. Are A and B mutually exclusive events? No, they are not Mutually Exclusive Yes, they are Mutually Exclusive d. Are A and B independent events? They are Independent events They are not Independent events

Answer 1

(a)

Total number of Events = 6 X 6 = 36

Favorable Events:
(2,2), (4,4), (6,2),

(2,3), (4,3), (6,3),

(2,4), (4,4), (6,4),

(2,5), (4,5), (6,5): 12 Nos.

So,

P(A) = 12/36 = 0.3333

(b)

Total number of Events = 6 X 6 = 36

Favorable Events:

(1,6), (6,1), (2,5), (5,2), (3,4), (4,3): 6 Nos.

So,

P(B) = 6/36 = 0.1667

(c)

Correct option:

No, they are not Mutually Exclusive

Explanation:

Events A and B can occur together: For example: (4,3) satisfies both Events A and B.

(d)

They are not independent events

Explanation:
For P(AB):

Favorable Events: (4,3): 1 Nos.

So,

P(AB) = 1/36 = 0.0278

P(A) X P(B) = 0.3333 X 0.1667 = 0.0556

Since P(AB) = 0.0278 P(A) X P(B) = 0.0556, Events A and B are not independent.