Roll two dice, one white and one red. Consider these events: A : The sum is 7 B : The white die is odd C : The red die has a larger number showing than the white D : The dice match (doubles) Which pair (s) of events are disjoint (events A and B are disjoint if A ∩ B = ∅) ? Which pair (s) are independent? Which pair (s) are neither disjoint nor independent?

Question

Mathematics

Serena Ochoa

5 April, 04:52

Roll two dice, one white and one red. Consider these events: A : The sum is 7 B : The white die is odd C : The red die has a larger number showing than the white D : The dice match (doubles) Which pair (s) of events are disjoint (events A and B are disjoint if A ∩ B = ∅) ? Which pair (s) are independent? Which pair (s) are neither disjoint nor independent?

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Kosmo · Answer 1

Step-by-step explanation:

Roll two dice, one white and one red

A = The sum of 7 = [ (3,4), (4,3), (2,5), (5,2), (6,1), (1,6) ]

B = the white die is odd = [ (1,1), (1,3), (1,5), (2,1), (2,3), (2,5), (6,1), (6,3), (6,5), (3,1), (3,3), (3,5), (4,1), (4,3), (4,5), (5,1), (5,3), (5,5) ]

C = Red die has larger number; [ (1,1), (2,2), (3,3), (4,4), (5,5), (6,6) ]

a) AnC = ∅ disjoint

b) P (A) = 1/6, P (B) = 1/2, P (C) = 1/6

P (AnB) = 1/12, P (AnC) = 1/36, P (BnC) = 1/12

A and B, B and C are independent