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Urn 1 contains 6 red balls and 2 black balls. Urn 2 contains 2 red balls and 2 black balls. Urn 3 contains 5 red balls and 2 black balls. If an urn is selected at random and a ball is drawn, find the probability that it will be red.

 Apr 11, 2020
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Urn 1 has 6 red balls and 2 black balls (total = 8 balls)

--  the probability of drawing a red ball from this urn is 6/8.

Urn 2 has 2 red balls and 2 black balls (total = 4 balls)

--  the probability of drawing a red ball from this urn is 2/4.

Urn 3 has 5 red balls and 2 black balls (total = 7 balls)

--  the probability of drawing a red ball from this urn is 5/7.

 

Since an urn is selected at random, the probability of drawing each urn is 1/3.

 

To find the final probability of selecting a red ball: for each urn -- multiply the probability of drawing an urn

times the probability of drawing a red ball from that urn, and add these three answers together.

 

Total proability:  (1/3)(6/8) + (1/3)(2/4) + (1/3)(5/7)  =  0.655

 Apr 11, 2020

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