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?

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

step-by-step explanation:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.

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step-by-step explanation:

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