# conditional probability

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You have two bags of marbles.

Bag 1 has 5 red and 6 blue marbles.
Bag 2 has 20 green and 5 red marbles.

What is the probability of drawing a red marble out of Bag 2, given that you drew a red marble out of Bag 1?

• conditional probability -

5/25 = 1/5

It makes no difference what color she drew from Bag 1.

• conditional probability -

P(R1)=5/11
P(R2)=5/25

Since the drawing of the two bags are independent, we have
P(R1∩R2)=P(R1)*P(R2)

P(R2|R1)=P(R2∩R1)/P(R1)
=P(R1)*P(R2)/P(R1)
=P(R2)

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