Arithmetic Ability
 Probability

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Q.

A bag contains 4 red and 3 black balls. A second bag contains 2 red and 4 black balls. One bag is selected at random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is red.

View Answer

Correct choice: B

Explanation:

A red ball can be drawn in two mutually exclusive ways (i) Selecting bag I and then drawing a red ball from it. (ii) Selecting bag II and then drawing a red ball from it. Let E1, E2 and A denote the events defined as follows: E1 = selecting bag I, E2 = selecting bag II A = drawing a red ball Since one of the two bags is selected randomly, therefore P(E1) = 1/2 and P(E2) = 1/2 Now, P(AE1) = Probability of drawing a red ball when the first bag has been selected = 4/7 P(AE2) = Probability of drawing a red ball when the second bag has been selected = 2/6 Using the law of total probability, we have P(red ball) = P(A) = P(E1)×P(A/E1)+P(E2)×P(A/E2) = 1/2×4/7+1/2×2/6=19/42
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