srikanth9502 wrote:
Thank you for the explanation.
I thought will be 2C2 x 5C2 X 3C2/10C6 (selection) multiplied by 6!/2!2!2!.
Can you please explain the error in my approach.
origen87 wrote:
mikeprobability = \(\tfrac{2}{10} \times \tfrac{2}{10} \times \tfrac{5}{10} \times \tfrac{5}{10} \times \tfrac{3}{10} \times \tfrac{3}{10}\) = \(\tfrac{10*10*3*3}{1000000}\) = \(\tfrac{9}{10000}\)
Wouldn't this be a case similar to choosing a marbel and putting it back in the box?
As the bulb once lit is no more a part of outcome I calcuated the probablity as below:
probability = \(\tfrac{2}{10} \times \tfrac{1}{9} \times \tfrac{5}{8} \times \tfrac{4}{7} \times \tfrac{3}{6} \times \tfrac{2}{5}\)
Please correct me.
Dear
srikanth9502 &
origen87,
I'm happy to respond.
Look at the text of the problem.
A string of lights is strung with red, blue, and yellow bulbs in a ratio of two to five to three, respectively. How many total bulbs are there? Just because there's a 2:5:3 ratio
does not mean that there are 10 and only 10 bulbs in total. That is the kind of concrete literalist thinking about ratios that the GMAT regularly punishes.
In fact, the total number of bulbs was not mentioned. All we are told is that there is a "
string of bulbs," a phrase that implies a large number of lights, and we have no idea how long this string is--maybe 12 ft, maybe 100 ft, maybe a mile. The implication is that we are dealing with a large
population of bulbs, a number of bulbs so large that, for all intents and purposes, picking doesn't change the ratios at all. If I pick one bulb, the probability of picking blue is 5/10 = 1/2, and even if I put that blue aside and pick from the remaining population, the probability is still essentially 1/2 of picking one more blue bulb. With populations, we no longer have to consider the distinction of picking with or without replacement: that's only meaningful in a group of relatively small size.
This is a somewhat more extreme example, but let's say if I pick a random human being, there is a 1/2 probability that I pick a male. Well, even if 20 male get together someplace, and as it were, eliminate themselves from selection pool and start looking at the probability of picking another male from the rest of humanity, there would still be a 1/2 probability of picking a male. The numbers of humans are so large that adding or subtracting another 20 doesn't make much of a different. Just for comparison, on average about 250 human people are born each minute and about 105 people die each minute on the global scale. In that context, 20 people is considerably less than the minute-by-minute error margin.
Of course, the population of bulbs is probably not as large as the total human population of 7+ billion, but the fact that no grand total was specified implies that it is very large--large enough that adding or subtracting a couple bulbs will not change the ratios in any meaningful way.
Does all this make sense?
Mike