Arithmetic Ability
 Probability

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Q.

An urn contains 4 white 6 black and 8 red balls . If 3 balls are drawn one by one without replacement, find the probability of getting all white balls.

View Answer

Correct choice: B

Explanation:

Let A, B, C be the events of getting a white ball in first, second and third draw respectively, then Required probability = P(A∩B∩C) = P(A) P(BA) P(CA∩B) Now, P(A) = Probability of drawing a white ball in first draw = 4/18 = 2/9 When a white ball is drawn in the first draw there are 17 balls left in the urn, out of which 3 are white ∴P(BA)=3/17 Since the ball drawn is not replaced, therefore after drawing a white ball in the second draw there are 16 balls left in the urn, out of which 2 are white. ∴P(CA∩B) =2/16=1/8 Hence the required probability = 2/9×3/17×1/8=1/204
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