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Here is a little warm-up quiz, based on the formula for conditional probability in Part A of this tutorial.

Which of the following are true for arbitrary events A, B, and C?

P(AB) = P(A)P(B)	True False		P(AB) = P(A|B)P(B)	True False
P(A|B) = P(A) P(B)	True False		P(BA) = P(B|A)P(B)	True False
P(A|C) = P(A|B) P(B|C)	True False		P(A|B)P(B) = P(B|A)P(A)	True False

Independent Events The events A and B are independent if any one of the following three equivalent conditions hold.             P(AB) = P(A)P(B) P(A|B) = P(A) B has no effect on A P(B|A) = P(B) A has no effect on B Intuitively, two events are independent if the occurrence of one has no effect on the probability of the other. If two events E and F are not independent, then they are dependent.

Example You throw two fair dice, one green and one red, and observe the numbers uppermost. A: the event that their sum is 7; P(E) = n(E)/36 = 6/36 = 1/6 B: the event that the red die shows an even number; P(F) = 1/2 P(AB) = P((1, 6), (3, 4), (5, 2)) = 3/36 = 1/12. Test for Independence P(AB) = P(A)P(B) ? 1 12 = 1 6 . 1 2 Therefore, the events are independent.

The following is similar to Exercsies 17-22 in Section 7.6 of Finite Mathematics and Finite Mathematics and Applied Calculus.

You throw two fair dice, one green and one red, and observe the numbers uppermost. Decide which of the following paris of events are indpendent.

Now try the exercises in Section 7.6 of Finite Mathematics, or Finite Mathematics and Applied Calculus.