unsinkable Posted June 3, 2010 Share Posted June 3, 2010 (edited) A jar contains 2 blue chips, 3 pink chips and 4 yellow chips. In the first trial, Sue picks one chip and doesn't return it to the jar. Then she chooses another chip. What is the probability both chips are blue? In a new trial with the same jar, Sue picks one chip, returns it and then draws another. What is the probability of choosing 2 blue chips? Thanks. UPDATE in last post! Edited June 4, 2010 by unsinkable update! Quote Link to comment Share on other sites More sharing options...
Caroline Posted June 3, 2010 Share Posted June 3, 2010 A jar contains 2 blue chips, 3 pink chips and 4 yellow chips. In the first trial, Sue picks one chip and doesn't return it to the jar. Then she chooses another chip. What is the probability both chips are blue? In a new trial with the same jar, Sue picks one chip, returns it and then draws another. What is the probability of choosing 2 blue chips? Thanks. The first trial: Since there are nine chips in the jar, the first time she pulls, she has a 2/9 probability of pulling a blue chip. Now there are only eight chips in the jar, and only one of them is blue. So she has a 1/8 probability of pulling a blue chip. You multiply the two probabilities together to get a probability of 2/72. The second trial: Again, the first time it is 2/9. Since she puts the chip back, there are still 2 blue chips and nine in the jar for the second pull, so again the probability is 2/9. Multiply them together and you get a probability of 4/81. Quote Link to comment Share on other sites More sharing options...
unsinkable Posted June 3, 2010 Author Share Posted June 3, 2010 The first trial: Since there are nine chips in the jar, the first time she pulls, she has a 2/9 probability of pulling a blue chip. Now there are only eight chips in the jar, and only one of them is blue. So she has a 1/8 probability of pulling a blue chip. You multiply the two probabilities together to get a probability of 2/72. The second trial: Again, the first time it is 2/9. Since she puts the chip back, there are still 2 blue chips and nine in the jar for the second pull, so again the probability is 2/9. Multiply them together and you get a probability of 4/81. Caroline, Thanks! Those were my DS's answers, too, but they were crossed out by his teacher...I can't figure it out...DS will have to ask him. What about this one: Factor completely: 24x^2 - 54 Quote Link to comment Share on other sites More sharing options...
Caroline Posted June 3, 2010 Share Posted June 3, 2010 Caroline, Thanks! Those were my DS's answers, too, but they were crossed out by his teacher...I can't figure it out...DS will have to ask him. What about this one: Factor completely: 24x^2 - 54 Well, probability is not my strong suit, but these seem pretty straight forward. 6(2x-3)(2x+3) is my guess on that last one. Or (2x3)(2x-3)(2x+3) Quote Link to comment Share on other sites More sharing options...
Dana Posted June 3, 2010 Share Posted June 3, 2010 Factor completely: 24x^2 - 54 Factor out the GCF first: 6 (4x^2 - 9) Now you have the difference of squares: a^2 - b^2 So your final complete factorization is 6 (2x-3)(2x+3) You always have to factor out the GCF first, otherwise your polynomial isn't completely factored. Quote Link to comment Share on other sites More sharing options...
unsinkable Posted June 3, 2010 Author Share Posted June 3, 2010 (edited) Well, probability is not my strong suit, but these seem pretty straight forward. 6(2x-3)(2x+3) is my guess on that last one. Or (2x3)(2x-3)(2x+3) Why wouldn't it be 6(4x^2 - 9) ? I am not sure about that?! DOH! Never mind. It's not factored completely. Bangs head on table. Edited June 3, 2010 by unsinkable Quote Link to comment Share on other sites More sharing options...
MyThreeSons Posted June 4, 2010 Share Posted June 4, 2010 I concur on all of the answers given. The only quibble I might have is that the first fraction (2/72) should be reduced to 1/36. Please let us know what your son's teacher says they ought to be and why. Quote Link to comment Share on other sites More sharing options...
unsinkable Posted June 4, 2010 Author Share Posted June 4, 2010 UPDATE: For the original probability problems: It was a clerical issue. :001_smile: I guess when the teacher originally handed out the paper, he told the boys to cross off that problem. DS was absent so he didn't cross it off. When the teacher corrected it, he scribbled a line thru DS's answer without even reading it b/c the problem didn't count. We mistook the teacher's scribbled line for an answer being marked wrong. It wasn't wrong. Did I explain it clearly enough? :lol: The factoring problem is me being an idiot. Or God showing me we all deserve patience and to show some algebra humility. Quote Link to comment Share on other sites More sharing options...
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