Question

On a single roll of two number cubes are rolling a sum of 6 and rolling doubles independent events?

Answer 1

Answer:0 they aren’t independent

Explanation:

A -> Rolling a sum of 6 (Can occur with (1,5), (5,1), (3,3), (2,4), (4,2)B -> Rolling Doubles (Can occur in 6 different ways)P(A) = 5/36P(B) = 6/36 = 1/6P(A)*P(B) = (5/36)*(1/36)= 5/1296P(A∩B) = 1/36 (This only happens when (3,3) is rolledIn this case,P(A)*P(B) =/= P(A∩B)Hence, they are not independent, which means that their occurence affects the others' probability.

Answer 2

Explanation:

A -> Rolling a sum of 6 (Can occur with (1,5), (5,1), (3,3), (2,4), (4,2)

B -> Rolling Doubles (Can occur in 6 different ways)

P(A) = 5/36

P(B) = 6/36 = 1/6

P(A)*P(B) = (5/36)*(1/36)

= 5/1296

P(A∩B) = 1/36 (This only happens when (3,3) is rolled

In this case,

P(A)*P(B) =/= P(A∩B)

Hence, they are not independent, which means that their occurence affects the others' probability.