SOLUTION: Please help? Two urns contain each contain white balls and black balls. Urn 1 contains four white balls and two black balls urn 2 contains six white balls and five black balls. A

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Question 40310: Please help?
Two urns contain each contain white balls and black balls. Urn 1 contains four white balls and two black balls urn 2 contains six white balls and five black balls. A ball is drawn from each urn. What is the probability that both balls are black?
Found 3 solutions by fractalier, Fermat, AnlytcPhil:
Answer by fractalier(6550)   (Show Source): You can put this solution on YOUR website!
The probability that both are black is the product of the probabilities that a black ball will be drawn from each...
So we have
2/6 * 5/11 = 10/66 = 5/33
Answer by Fermat(136)   (Show Source): You can put this solution on YOUR website!
Urn1: 4W & 2B
Urn2: 6W & 5B
P1 = P(Urn1 -> Black ball) (P1 is the probability that urn1 will give a black ball)
P2 = P(Urn2 -> Black ball) (P2 is the probability that urn2 will give a black ball)
P = P1 * P2 (P is the probability that both balls will be black)
Now,
In urn1, there are 6 balls in total, with 2 of them black, So,
P1 = 2/6
========
In urn2 there are 11 balls in total, with 5 of them black, So,
P2 = 5/11
=========
P = P1 * P2
P = (2/6) * (5/11)
P = 10/66
Ans: P = 5/33
=============
Answer by AnlytcPhil(1806)   (Show Source): You can put this solution on YOUR website!
Two urns contain each contain white balls and black balls. Urn 1 contains four
white balls and two black balls urn 2, contains six white balls and five black
balls. A ball is drawn from each urn. What is the probability that both balls
are black?

Urn 1 contains 6 balls, 2 of which are black, so the probability of drawing
a black ball from urn 1 is 2/6 or 1/3

Urn 2 contains 11 balls, 5 of which are black, so the probability of drawing
a black ball from urn 2 is 5/11

P(getting black ball from urn 1 AND getting black ball from urn 2) 

since these events are independent, we may multiply their probabilities

P(getting black ball from urn 1) × P(getting black ball from urn 2) =

1/3 × 5/11 = 5/33 

(or a little more than 15% of the time.)

Edwin
AnlytcPhil@aol.com
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