Question

Roll two fair dice. Each die has six faces.

A. Let A be the event that either a 3 or 4 is rolled first followed by an odd number. P(A) =  Round your answer to two decimal places.

B. Let B be the event that the sum of the two dice is at most 7. P(B) =  Round your answer to two decimal places.

C. Are A and B mutually exclusive events? (Yes or No)

D. Are A and B independent or dependent events? (Independent or Dependent)

Answer 1

There is a totalof 6*6 = 36 outcomes if you roll two die

(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)

a) Event A :

(3,1), (3,3), (3,5),
(4,1), (4,3), (4,5)

b) Event 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)

c) In probability theory, two events are mutually exclusive or disjoint if they cannot both occur at the same time.

Hence A and B are not mutually exclusive.

d) Two events are independent if the result of the second event is not affected by the result of the first event. If A and B are independent events, the probability of both events occurring is the product of the probabilities of the individual events.

Hence A and B are dependent events