Box contains 3 gold and 4 silver coins. Another box contains 2 gold and 3 silver coins. A box is chosen at random, and a coin is drawn from it. If the selected coin is a gold coin, find the probability that it was drawn from the second box.
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7/17 would be the probability of the gold coin being selected from the second box.
Step-by-step explanation:
Given that,
Let G be the gold coins while S as the silver
and the boxes to be A and B
G in box A = 3
S in box A = 4
G in box B = 2
S in box B= 3
Let the probability of selecting box as equal = 1/2
To find,
The Probability of the selected gold coin is from the second box = P(B/G)
P(B/G) = {(P(B) (P(G/B)}/P(A).P(G/A) + P(B). P(G/B)
= {(1/2) (2/5)}/{(4/7) (1/2) + (2/5) (1/2)
= (1/5)/{(4/14) + (2/10)}
= 7/17
Thus, 7/17 is the probability of taking the gold coin from the second box.
Learn more: find the probability
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