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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 ## Probability ##### This topic has 4 expert replies and 3 member replies ## Probability The probability that A will successfully hit a target is 2/3. The probability of B succesfully hitting a target is 2/3. if they shoot two shots each then what is the probability that they have an equal number of hits? ### Top Member Master | Next Rank: 500 Posts Joined 15 Oct 2009 Posted: 330 messages Upvotes: 27 11/27 Newbie | Next Rank: 10 Posts Joined 10 Mar 2016 Posted: 7 messages regor60 wrote: 11/27 Hi could you please give the exact solution how you get 11/27 ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15387 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 mallireddy wrote: The probability that A will successfully hit a target is 2/3. The probability of B succesfully hitting a target is 2/3. if they shoot two shots each then what is the probability that they have an equal number of hits? AND means MULTIPLY. OR means ADD. Case 1: Each hits the target 0 times P(A misses the 1st shot AND the 2nd shot) = 1/3 * 1/3 = 1/9. P(B misses the 1st shot AND the 2nd shot) = 1/3 * 1/3 = 1/9. Since a favorable result requires that A miss both shots (1/9) AND that B miss both shots (1/9), we MULTIPLY the fractions in red: 1/9 * 1/9 = 1/81. Case 2: Each hits the target once P(A hits the 1st shot AND misses the 2nd shot) = 2/3 * 1/3 = 2/9. P(A misses the 1st shot AND hits the 2nd shot) = 1/3 * 2/3 = 2/9. Since a favorable result requires that A hit only the 1st shot (2/9) OR that A hit only the 2nd shot (2/9), we ADD the fractions in red: 2/9 + 2/9 = 4/9. P(B hits the 1st shot AND misses the 2nd shot) = 2/3 * 1/3 = 2/9. P(B misses the 1st shot AND hits the 2nd shot) = 1/3 * 2/3 = 2/9. Since a favorable result requires that B hit only the 1st shot (2/9) OR that B hit only the second shot (2/9), we ADD the fractions in red: 2/9 + 2/9 = 4/9. Since a favorable result requires that A hit the target exactly once (4/9) AND that B hit the target exactly once (4/9), we MULTIPLY the fractions in blue: 4/9 * 4/9 = 16/81. Case 3: Each hits the target twice P(A hits the first shot AND the 2nd shot) = 2/3 * 2/3 = 4/9. P(B hits the first shot AND the 2nd shot) = 2/3 * 2/3 = 4/9. Since a favorable result requires that A hit both shots (4/9) AND that B hit both shots (4/9), we MULTIPLY the fractions in red: 4/9 * 4/9 = 16/81. Since a favorable outcome will be yielded by Case 1 OR Case 2 OR Case 3, we ADD the fractions in green: 1/81 + 16/81 + 16/81 = 33/81 = 11/27. _________________ 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. Newbie | Next Rank: 10 Posts Joined 10 Mar 2016 Posted: 7 messages Thanks for prompt reply Guru I have one doubt regarding probability tried a lot to get it solved but I can't find one good answer Here it is Case1:Sample space when 3 different coins tossed simultaneously is {HHH,TTT,HHT,THH,HTT,THH,THT,HTH} Case2:Sample space when 3 different coins tossed not simultaneously is also taken as {HHH,TTT,HHT,THH,HTT,THH,THT,HTH}. In case2 suppose if we take 3 coins as A,B,C here we have 3! different ways for to toss them and for each way the possible outcomes are {HHH,TTT,HHT,THH,HTT,THH,THT,HTH} so we have 6*8 as Total outcomes but,why people are not considering this 6*8 and considering Total outcomes as 8? why different ways of throwing coins are being neglected? Thanks in advance ### GMAT/MBA Expert GMAT Instructor Joined 12 Sep 2012 Posted: 2635 messages Followed by: 117 members Upvotes: 625 Target GMAT Score: V51 GMAT Score: 780 mallireddy wrote: The probability that A will successfully hit a target is 2/3. The probability of B succesfully hitting a target is 2/3. if they shoot two shots each then what is the probability that they have an equal number of hits? This should be (Each has 0 hits) + (Each has exactly 1 hit) + (Each has exactly 2 hits) or (1/3)*(1/3)*(1/3)*(1/3) + 2*(2/3)*(1/3)*2*(2/3)*(1/3) + (2/3)*(2/3)*(2/3)*(2/3) or 1/81 + 16/81 + 16/81 or 33/81 => 11/27 Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now! ### GMAT/MBA Expert GMAT Instructor Joined 12 Sep 2012 Posted: 2635 messages Followed by: 117 members Upvotes: 625 Target GMAT Score: V51 GMAT Score: 780 mallireddy wrote: In case2 suppose if we take 3 coins as A,B,C here we have 3! different ways for to toss them and for each way the possible outcomes are {HHH,TTT,HHT,THH,HTT,THH,THT,HTH} so we have 6*8 as Total outcomes but,why people are not considering this 6*8 and considering Total outcomes as 8? why different ways of throwing coins are being neglected? Thanks in advance You're conflating two cases here: in the first case, you're assuming that the coins are all identical, and only H/T matters, but in the second, you're assuming that the coins are somehow different (e.g. they have three different colors, or three different sets of faces, or three different denominations of coin, etc.), which would give you a greater number of meaningfully distinct results to consider. Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now! ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15387 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 mallireddy wrote: Thanks for prompt reply Guru I have one doubt regarding probability tried a lot to get it solved but I can't find one good answer Here it is Case1:Sample space when 3 different coins tossed simultaneously is {HHH,TTT,HHT,THH,HTT,THH,THT,HTH} Case2:Sample space when 3 different coins tossed not simultaneously is also taken as {HHH,TTT,HHT,THH,HTT,THH,THT,HTH}. In case2 suppose if we take 3 coins as A,B,C Thanks in advance in your lists above, one possible outcome -- THH -- is included twice. The lists above should read as follows: {HHH,TTT,HHT,THH,HTT,TTH,THT,HTH} In Case 2, this list includes every possible outcome for coins A, B and C: HHH: A --> heads, B --> heads, C --> heads TTT: A --> tails, B --> tails, C --> tails HHT: A --> heads, B --> heads, C --> tails THH: A --> tails, B --> heads, C --> heads HTT: A --> heads, B --> tails, C --> tails TTH: A --> tails, B --> tails, C --> heads THT: A --> tails, B --> heads, C --> tails HTH: A --> heads, B --> tails, C --> heads Green outcomes = all 3 coins are the same Blue outcomes = only C is tails, only A is tails, only B is tails Red outcomes = only A is heads, only C is heads, only B is heads Total number of possible outcomes = (green outcomes) + (blue outcomes) + (red outcomes) = 2 + 3 + 3 = 8. Quote: here we have 3! different ways for to toss them and for each way the possible outcomes are {HHH,TTT,HHT,THH,HTT,TTH,THT,HTH} so we have 6*8 as Total outcomes but,why people are not considering this 6*8 and considering Total outcomes as 8? why different ways of throwing coins are being neglected? As I've shown above, the list in red includes every possible outcome for coins A, B and C. Thus, there is no reason to multiply by 3!. _________________ 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! 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