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0 votes
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in Mathematics by (71.5k points)

Bag I contains 6 white and 4 black balls while another Bag II contains 3 white and 4 black balls. One ball is drawn at random from one of the bags and it is found to be black. What is the probability that it was drawn from Bag II? 

(a) 0.404 

(b) 0.583 

(c) 0.588 

(d) 0.644

1 Answer

+1 vote
by (65.1k points)
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Best answer

Correct option (c) (0.588)

Explanation:

Let E1 be the event of choosing the bag I, E2 the event of choosing the bag II and A be the event of drawing a black ball.

Then, P(E1) = P(E2) = 1/2 

Also, P(A|E1 ) = P(drawing a black ball from Bag I) = 4/10 = 2/5

P(A|E2) = P(drawing a black ball from Bag II) = 4/7

By using Bayes’ theorem, the probability of drawing a black ball from bag II out of two bags,

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