Each urn is selected with probability  so we multiply that by the probability of selecting red from each urn, and add them:







which works out to   or about 0.687  (68.7% chance to pick red)



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EDIT:  Oops, thanks tutor ikleyn.  To check my answer, I had calculated the probability of obtaining black (0.313) and accidently copied down that calculation.   

Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
 .

Urn 1 contains 7 red balls and 4 black balls. 

Urn 2 contains 4 red balls and 1 black ball. 

Urn 3 contains 5 red balls and 3 black balls. 

If an urn is selected at random and a ball is drawn, find the probability that it will be red.

~~~~~~~~~~~~~~







            I came to fix incorrect writing  (typos ?)  in the post by @math_helper.







    P(red) =  +  +  = 


           =  =  = 


           =  = .    ANSWER




Solved.







 

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