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Retired Moderator Joined: 27 Aug 2012 Posts: 1029
Math Expert Joined: 02 Sep 2009 Posts: 86662
Re: A jar contains 4 black and 3 white balls.If you pick two [#permalink]
bagdbmba wrote: A jar contains 4 black and 3 white balls. If you pick two balls at the same time, what's the probability that one ball is black and one is white?A. 2/7B. 5/7C. 4/7D. 3/7 E. 1/2 P(1st black, 2nd white) = 4/7*3/6 = 4/14;P(1st white, 2nd black) = 3/7*4/6 = 4/14.P = 4/14 + 4/14 = 4/7.Answer: C.OR: \(P=\frac{C^1_4*C^1_3}{C^2_7}=\frac{4}{7}\)OA is NOT correct. _________________
Retired Moderator Joined: 27 Aug 2012 Posts: 1029
Re: A jar contains 4 black and 3 white balls.If you pick two [#permalink]
Bunuel wrote: bagdbmba wrote: A jar contains 4 black and 3 white balls. If you pick two balls at the same time, what's the probability that one ball is black and one is white?A. 2/7B. 5/7C. 4/7D. 3/7 E. 1/2 P(1st black, 2nd white) = 4/7*3/6 = 4/14;P(1st white, 2nd black) = 3/7*4/6 = 4/14.P = 4/14 + 4/14 = 4/7.Answer: C.OR: \(P=\frac{C^1_4*C^1_3}{C^2_7}=\frac{4}{7}\)OA is NOT correct. Hi Bunuel,As per the above explanation - why the OA of the following problem is NOT 3/10?http://gmatclub.com/forum/x-y-and-z-are-all-unique-numbers-if-x-is-chosen-randomly-159208.html Would you please help? _________________
Manager Joined: 23 May 2013 Posts: 78
Re: A jar contains 4 black and 3 white balls.If you pick two [#permalink]
Bunuel wrote: bagdbmba wrote: A jar contains 4 black and 3 white balls. If you pick two balls at the same time, what's the probability that one ball is black and one is white?A. 2/7B. 5/7C. 4/7D. 3/7 E. 1/2 P(1st black, 2nd white) = 4/7*3/6 = 4/14;P(1st white, 2nd black) = 3/7*4/6 = 4/14.P = 4/14 + 4/14 = 4/7.Answer: C.OR: \(P=\frac{C^1_4*C^1_3}{C^2_7}=\frac{4}{7}\)OA is NOT correct. Hi BunuelI wanted to know if probability approach can be used to resolve any sort of probability problem. I am quite comfortable with it. when is it advantageous to use combination approach?
Re: A jar contains 4 black and 3 white balls. If you pick two ba [#permalink]
Bunuel wrote: bagdbmba wrote: A jar contains 4 black and 3 white balls. If you pick two balls at the same time, what's the probability that one ball is black and one is white?A. 2/7B. 5/7C. 4/7D. 3/7 E. 1/2 P(1st black, 2nd white) = 4/7*3/6 = 4/14;P(1st white, 2nd black) = 3/7*4/6 = 4/14.P = 4/14 + 4/14 = 4/7.Answer: C.OR: \(P=\frac{C^1_4*C^1_3}{C^2_7}=\frac{4}{7}\)OA is NOT correct. Hello Bunuel and VeritasPrepKarishma As per Veritas the answer is 2/7And the logical argument is that event is happening simultaneously hence we will only consider one scenario of removing the balls.Could you please confirm what should be the correct strategy and what is the correct answer?We are now confused between 4/7 & 2/7 _________________
"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent." Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475
Math Expert Joined: 02 Sep 2009 Posts: 86662
Re: A jar contains 4 black and 3 white balls. If you pick two ba [#permalink]
ydmuley wrote: Bunuel wrote: bagdbmba wrote: A jar contains 4 black and 3 white balls. If you pick two balls at the same time, what's the probability that one ball is black and one is white?A. 2/7B. 5/7C. 4/7D. 3/7 E. 1/2 P(1st black, 2nd white) = 4/7*3/6 = 4/14;P(1st white, 2nd black) = 3/7*4/6 = 4/14.P = 4/14 + 4/14 = 4/7.Answer: C.OR: \(P=\frac{C^1_4*C^1_3}{C^2_7}=\frac{4}{7}\)OA is NOT correct. Hello Bunuel and VeritasPrepKarishma As per Veritas the answer is 2/7And the logical argument is that event is happening simultaneously hence we will only consider one scenario of removing the balls.Could you please confirm what should be the correct strategy and what is the correct answer?We are now confused between 4/7 & 2/7 Mathematically the probability of picking two balls simultaneously, or picking them one at a time (without replacement) is the same. The correct answer is 4/7. _________________
Re: A jar contains 4 black and 3 white balls. If you pick two ba [#permalink] Hello Bunuel and VeritasPrepKarishmaAs per Veritas the answer is 2/7And the logical argument is that event is happening simultaneously hence we will only consider one scenario of removing the balls.Could you please confirm what should be the correct strategy and what is the correct answer?We are now confused between 4/7 & 2/7[/quote] Bunuel wrote:
Ok.. thanks Bunuel - will go with 4/7 VeritasPrepKarishma - Not sure if you agree to this, in case the books have to be changed to avoid confusion going forward. _________________
"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent." Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475
GMAT Expert Joined: 16 Oct 2010 Posts: 13085 Location: Pune, India
A jar contains 4 black and 3 white balls. If you pick two ba [#permalink]
ydmuley wrote: Hello Bunuel and VeritasPrepKarishmaAs per Veritas the answer is 2/7And the logical argument is that event is happening simultaneously hence we will only consider one scenario of removing the balls.Could you please confirm what should be the correct strategy and what is the correct answer? We are now confused between 4/7 & 2/7 Bunuel wrote: Mathematically the probability of picking two balls simultaneously, or picking them one at a time (without replacement) is the same. The correct answer is 4/7. Ok.. thanks Bunuel - will go with 4/7 VeritasPrepKarishma - Not sure if you agree to this, in case the books have to be changed to avoid confusion going forward. Responding to a pm:The answer is certainly 4/7 and that is what the book says too. The book shows that "2 simultaneous picks" is the same as "pick one and then another". So getting one black and one white can be achieved in 2 ways: a black and then a white or a white and then a black. I agree that the addition isn't explicitly shown but "pick two such that one is black and one is white" is composed of two cases:First black and then white for which Probability = 2/7First white and then black for which Probability = 2/7They both result in one white and one black so answer would be 4/7.Note that there are only 2 other cases:Both black for which probability = 4/7 * 3/6 = 2/7Both white for which probability = 3/7 * 2/6 = 1/7Overall probability = 2/7 + 2/7 + 2/7 + 1/7 = 1 _________________
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Re: A jar contains 4 black and 3 white balls. If you pick two ba [#permalink] Probability of both balls being Black = 4/7*3/6 = 2/7,Probability of both balls being White = 3/7* 2/6= 1/7 Probability of 1 white one black = 1- (2/7+17) = 4/7
Re: A jar contains 4 black and 3 white balls. If you pick two ba [#permalink] 29 Oct 2021, 07:35 |
A jar contains three white balls and two black balls each time you pick
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