SOLUTION: the constitution of 2 urns: first urn has 3 black balls and 2 whites second urn has 4 black balls and 6 whites. -> a draw is made by selecting an urn by a process which assigns p

Question 471378: the constitution of 2 urns: first urn has 3 black balls and 2 whites
second urn has 4 black balls and 6 whites.
-> a draw is made by selecting an urn by a process which assigns probability P to the selection of urn I and probability 1-P to the selection of urn II. the selection of a ball from either urn is by a process which assigns equal probability to all balls in the urn. what value of P makes the probability of obtaining a black ball the same as if a single draw were made from an urn with 7 balck balls and 8 white balls (all balls are equally probable of being drawn).
thank you!
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
The equation is

<==>
==> 3p + 2(1-p) = 7/3, after multiplication by 5.
==> 3p + 2 - 2p = 7/3
==> p = 7/3-2
==> p = 1/3.
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