brindha_arun Posted June 12, 2005 Share Posted June 12, 2005 There are two identical bottles. One bottle contains 2 green balls and 1 red ball. The other contains 2 red balls. A bottle is selected at random and a single ball is drawn. What is the probability that the ball is red? ans:!/2 1/6 2/3 1/3 I will post the right answers after the responses Quote Link to comment Share on other sites More sharing options...
ish Posted June 12, 2005 Share Posted June 12, 2005 its D Quote Link to comment Share on other sites More sharing options...
brindha_arun Posted June 12, 2005 Author Share Posted June 12, 2005 Hi ish! You rock! I follow almost all ur posts! congrats on ur gr8 score! the answer is not d ! Its 2/3 Actually iam also perplexed how its 2/3 its D Quote Link to comment Share on other sites More sharing options...
ish Posted June 12, 2005 Share Posted June 12, 2005 Thanks Brinda oops sorry.i meant 2/3. i saw that it was the last but one choice and put in D. this is how its 2/3 There are two identical bottles. One bottle contains 2 green balls and 1 red ball. The other contains 2 red balls. A bottle is selected at random and a single ball is drawn. What is the probability that the ball is red? you can choose a red ball by choosing the first bottle OR the second one. The prob for choosing a bottle is 1/2. Say we choose the first one. choosing a red ball from that one is 1/3, so the total prob for the first bottle is (1/2)(1/3) suppose I choose the second bottle. Prob for doin that is 1/2 as well. Choosing a red one from the second one is done in 2/2 ways. Total prob is (1/2)(2/2) Add them up, 1/6 + 1/2 is 2/3. Quote Link to comment Share on other sites More sharing options...
samy_dg Posted June 12, 2005 Share Posted June 12, 2005 Required probability =(Probability that 1st bottle is chosen & ball is red)+(Probability that 2nd bottle is chosen & ball is red) =(1/2)X(1/3)+(1/2)X(1) =2/3. Quote Link to comment Share on other sites More sharing options...
brindha_arun Posted June 12, 2005 Author Share Posted June 12, 2005 WOW! great expln. thanks try out this one If a three digit number is formed from the digits 1,2,3,4,5,6, and 7, with no repetitions, tell how manyof these three digit numbers will have a number value between 100 and 500. my answer is 120 pl verify my anwer Required probability =(Probability that 1st bottle is chosen & ball is red)+(Probability that 2nd bottle is chosen & ball is red) =(1/2)X(1/3)+(1/2)X(1) =2/3. Quote Link to comment Share on other sites More sharing options...
ish Posted June 12, 2005 Share Posted June 12, 2005 I got 120 as well. This is a good Q. Quote Link to comment Share on other sites More sharing options...
brindha_arun Posted June 12, 2005 Author Share Posted June 12, 2005 Hi ish, I am really pushing myself hard in math. Being a life science graduate, I feel the difficulty in math esply in stats, probability, A.p , g,p . can u give me some suggestions to improve my skills in these. suggestion of any materials or websites or any posts would also be gr8. brindha I got 120 as well. This is a good Q. Quote Link to comment Share on other sites More sharing options...
ish Posted June 12, 2005 Share Posted June 12, 2005 There are a LOT of probability and stats sums in the GMAT PS section in TM. Visit that everytime you log in to TM. Work on the PP math review for some stats sums. Its a good indicator for stats. if you have time on your hands, become a member at number2.com and work on their tutorials. its a good service. i dont have many links for math, most of them are for verbal.check our yahoo mailbox, i saw some Quants files there that may help you. good luck:) and work on your speed. you should be fast. :) Quote Link to comment Share on other sites More sharing options...
brindha_arun Posted June 12, 2005 Author Share Posted June 12, 2005 The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up heads? There are two identical bottles. One bottle contains 2 green balls and 1 red ball. The other contains 2 red balls. A bottle is selected at random and a single ball is drawn. What is the probability that the ball is red? ans:!/2 1/6 2/3 1/3 I will post the right answers after the responses Quote Link to comment Share on other sites More sharing options...
brindha_arun Posted June 12, 2005 Author Share Posted June 12, 2005 On any day in April in a certain city, the probability of rain is 50%. What is the probability of that it rains exactly 5 days during a 7 day period in April? The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up heads? Quote Link to comment Share on other sites More sharing options...
dsaqwert Posted June 12, 2005 Share Posted June 12, 2005 The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up heads? 1-(1/2)^3=7/8 Quote Link to comment Share on other sites More sharing options...
dsaqwert Posted June 12, 2005 Share Posted June 12, 2005 On any day in April in a certain city, the probability of rain is 50%. What is the probability of that it rains exactly 5 days during a 7 day period in April? 7c5/2^7 Quote Link to comment Share on other sites More sharing options...
manasi4gre Posted June 12, 2005 Share Posted June 12, 2005 On any day in April in a certain city, the probability of rain is 50%. What is the probability of that it rains exactly 5 days during a 7 day period in April? Ans= 7c5/2^7 Can u give an explaination, dsaqwert? Quote Link to comment Share on other sites More sharing options...
brindha_arun Posted June 12, 2005 Author Share Posted June 12, 2005 Hey can u explain ur strategy? 1-(1/2)^3=7/8 Quote Link to comment Share on other sites More sharing options...
dsaqwert Posted June 12, 2005 Share Posted June 12, 2005 Can u give an explaination, dsaqwert? in consequtive 7 days, every day has two possibility, either it rains or not, so 7 days have 2^7 different scenarios in terms of rainy days. and in seven days there is 7c5 different ways that only 5 days is rainy so 7c5/2^7 Quote Link to comment Share on other sites More sharing options...
dsaqwert Posted June 12, 2005 Share Posted June 12, 2005 Hey can u explain ur strategy? at least one head in three tosses means all the probabilities - no head in three tosses all possible outcomes has 1 probability and no head means three tails (TTT) which has probability (1/2)^3 so 1-(1/2)^3 Quote Link to comment Share on other sites More sharing options...
manasi4gre Posted June 12, 2005 Share Posted June 12, 2005 in consequtive 7 days, every day has two possibility, either it rains or not, so 7 days have 2^7 different scenarios in terms of rainy days. and in seven days there is 7c5 different ways that only 5 days is rainy so 7c5/2^7 It is pretty clear now.:) Quote Link to comment Share on other sites More sharing options...
Dkumar Posted June 12, 2005 Share Posted June 12, 2005 The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up heads? The answer is 3/8. Quote Link to comment Share on other sites More sharing options...
Dkumar Posted June 12, 2005 Share Posted June 12, 2005 The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up heads? The answer is 3/8 Quote Link to comment Share on other sites More sharing options...
Dkumar Posted June 12, 2005 Share Posted June 12, 2005 Hi Brinda! I get a different answer for your question. On any day in April in a certain city, the probability of rain is 50%. What is the probability of that it rains exactly 5 days during a 7 day period in April? Acc to my calculation, Probability that it will rain in a any day is 1/2 Prabability that it will not rain is (1-1/2) = 1/2 Probability that it will rain exactly 5 days and will not rain the other two days = 1/2 *1/2*1/2*1/2*1/2*1/2*1/2 = 1/128 Please let me know the correct answer. Thanks. Quote Link to comment Share on other sites More sharing options...
manasi4gre Posted June 12, 2005 Share Posted June 12, 2005 The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up heads? The answer is 3/8. How did u get this answer? Quote Link to comment Share on other sites More sharing options...
ish Posted June 12, 2005 Share Posted June 12, 2005 Hi Brinda! I get a different answer for your question. On any day in April in a certain city, the probability of rain is 50%. What is the probability of that it rains exactly 5 days during a 7 day period in April? Acc to my calculation, Probability that it will rain in a any day is 1/2 Prabability that it will not rain is (1-1/2) = 1/2 Probability that it will rain exactly 5 days and will not rain the other two days = 1/2 *1/2*1/2*1/2*1/2*1/2*1/2 = 1/128 Please let me know the correct answer. Thanks. Kumar,you have to use the binomial method here. nCr(p)^r(q)^n-r so here its 7C2(50/100)5(50/100)2 which is 21(1/2)^7 Quote Link to comment Share on other sites More sharing options...
manasi4gre Posted June 12, 2005 Share Posted June 12, 2005 ish, why cant we use the other approach? Quote Link to comment Share on other sites More sharing options...
ish Posted June 12, 2005 Share Posted June 12, 2005 because you have to account for the number of ways you can choose 5 out of 7, and then compute their respective probabilities. its also a question of choice, isnt it? Quote Link to comment Share on other sites More sharing options...
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