Question

Question 3 (1 point) Use following diagram to answer the question . Let A represents the event that the left die shows a multiple of 3. Let B represents the event that the right die shows an even number. Which of the following is true? A and B are disjoint and independent A and B are disjoint but not independent e Oo hp

Answer 1

We are given the 2 events here:

• A: Left die shows a multiple of 3 that is either 3 or 6.
  Therefore,
  A = { 31, 32, 33, 34, 35, 36, 61, 62, 63, 64, 65, 66}, that is 12 outcomes.
• B: Right die shows an even number that is either 2, 4 or 6.
  B = { 12, 14, 16, 22, 24, 26, 32, 34, 36, 42, 44, 46, 52, 54, 56, 62, 64, 66}, that is 18 outcomes.

Common elements in A and B: 32, 34, 36, 62, 64, 66.

As there are 6 common elements here, therefore the two events are not disjoint events here.

P(A) = 12/36 = 1/3
P(B) = 18/36 = 0.5
P(A)P(B) = 0.5/3 = 1/6

Also, P(A and B) = 6/36 = 1/6 which is equal to P(A)P(B), therefore A and B are independent events.

Therefore A and B are not disjoint events but independent events.