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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## If a bowl contains only white and black balls, what is the tagged by: vinni.k ##### This topic has 2 expert replies and 1 member reply ### Top Member ## If a bowl contains only white and black balls, what is the If a bowl contains only white and black balls, what is the probability of extracting a white ball from the bowl? (1) There are twice as many white balls as black balls in the bowl (2) If two balls are extracted from the bowl, the probability that both of them will be black is 0. OA is A Given: Bowl = only white + only black Question: P(extracting white ball) = White/(White + Black) (1) White = 2*Black P(extracting white ball) = 2*Black/(2*Black + Black) = 2/3 So, s(1) is sufficient. (2) Here, i am not able to interpret this statement properly. P(extracting both balls black) = Black/(White + Black) * (Black - 1)/(White + Black - 1) = 0 How to proceed from here ? It is given that the bowl contains only white and only black balls, it means that there are some black balls in the bowl, then how come the probability of extracting both black balls is 0. Please help me in understanding s(2). I don't know what i am missing here. Thank you. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 14929 messages Followed by: 1855 members Upvotes: 13060 GMAT Score: 790 Top Reply vinni.k wrote: If a bowl contains only white and black balls, what is the probability of extracting a white ball from the bowl? (1) There are twice as many white balls as black balls in the bowl (2) If two balls are extracted from the bowl, the probability that both of them will be black is 0. Statement 1: Of every 3 balls, 1 is black and 2 are white. Thus, the probability of extracting a white ball = 2/3. SUFFICIENT. Statement 2: Implication: The bowl contains at most 1 black ball, with the result that it is not possible to extract 2 black balls from the bowl. Case 1: 1 black ball and 1 white ball In this case, the probability of extracting a white ball = 1/2. Case 1: 1 black ball and 2 white balls In this case, the probability of extracting a white ball = 2/3. Since the probability can be different values, INSUFFICIENT. The correct answer is A. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 14929 messages Followed by: 1855 members Upvotes: 13060 GMAT Score: 790 Top Reply vinni.k wrote: Mitch, Just to confirm my understanding. S(2), if two balls are extracted from the bowl, the probability that both of them will be black is 0 I am just focusing only on this statement. As you have mentioned that the bowl contains at most 1 black ball. So, we have two cases. Case 1: for the probability to be 0, the bowl can have 0 black balls. Case 2: for the probability to be 0, the bowl can have 1 black ball. If the bowl has more than 1 black ball, then probability will not be 0. Am i correct ? Correct! _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### Top Member Master | Next Rank: 500 Posts Joined 17 Apr 2011 Posted: 420 messages Followed by: 2 members Upvotes: 6 Test Date: 2016 Target GMAT Score: 700+ GMAT Score: 620 Mitch, Just to confirm my understanding. S(2), if two balls are extracted from the bowl, the probability that both of them will be black is 0 I am just focusing only on this statement. As you have mentioned that the bowl contains at most 1 black ball. So, we have two cases. Case 1: for the probability to be 0, the bowl can have 0 black balls. Case 2: for the probability to be 0, the bowl can have 1 black ball. If the bowl has more than 1 black ball, then probability will not be 0. 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