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Probability

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by MBA.Aspirant » Sat Jun 18, 2011 3:41 pm
Of the 700 members of an org, 120 are lawyers. Two members will be selected at random. Which of the following is closest to the probability that neither of the members selected will be a lawyer?

0.5
0.6
0.7
0.8
0.9

Now you can do it 580/700 * 579/699 = ~ 0.7

but I wanted to do it subtracted from 1. So well it be 1- [ 120/700 * 119/699]

or

1- [ (120/700 * 119/699)+ 120/700]

Thanks
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by Brent@GMATPrepNow » Sat Jun 18, 2011 7:03 pm
MBA.Aspirant wrote:Of the 700 members of an org, 120 are lawyers. Two members will be selected at random. Which of the following is closest to the probability that neither of the members selected will be a lawyer?
0.5
0.6
0.7
0.8
0.9
Now you can do it 580/700 * 579/699 = ~ 0.7

but I wanted to do it subtracted from 1. So well it be 1- [ 120/700 * 119/699]

or

1- [ (120/700 * 119/699)+ 120/700]

Thanks
Your first method is correct:
P(neither is a lawyer) = P(first is not a lawyer AND second is not a lawyer)
= P(first is not a lawyer) x P(second is not a lawyer, given that the first is not a lawyer)
= 580/700 x 579/699 ~ 0.7


Your second method doesn't use the complement correctly.
Your calculations suggest that are saying that P(neither is a lawyer) = 1 - P(both are lawyers) and this is not correct.
1 - P(both are lawyers) is the probability that both selected people are not lawyers, which is not the same as neither selected person is a lawyer.

The case were both selected people are not lawyers can include:
a) the first person is not a lawyer and the second person is a lawyer
b) the first person is a lawyer and the second person is not a lawyer
c) neither person is a lawyer.

In the question, we are concerned only with c), which means your calculation includes two extra cases.

Cheers,
Brent
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by winniethepooh » Sun Jun 19, 2011 12:46 am
Thanks for your help, Brent. I really appreciate it. I have a couple of questions, if you can answer!
So what should the equation otherwise be? I mean to deduct the probability from 1(With numbers, if possible).

Also, as clearly visible 580 x 579/ 700 x 699 is a heavy calculation task, is there any way to make it easier(or some short calculation method)?
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by Brent@GMATPrepNow » Sun Jun 19, 2011 5:55 am
Also, as clearly visible 580 x 579/ 700 x 699 is a heavy calculation task, is there any way to make it easier(or some short calculation method)
Good question.
Here's one method. First recognize that 580/700 and 579/699 are pretty much equal (close enough for this question), so let's just calculate (580/700)(580/700)

Also recognize that 580/700 = 58/70 = 29/35

Now 28/35 = 0.8, so 0.8 is a little bit bigger than 0.8, which we can write as 0.8+

So, (580/700)(580/700) = (0.8+)(0.8+) = 0.64+ (the product is greater than 0.64)

At this point, we need to use some number sense to see that the product will be closer to 0.7 than to 0.6

So what should the equation otherwise be? I mean to deduct the probability from 1(With numbers, if possible).
Here I'll use L1 to denote selecting a lawyer on the first selection and N1 to denote not selecting a lawyer on the first selection.

So, P(neither is a lawyer) = 1 - P(at least one is a lawyer)
= 1 - P(L1L2 OR L1N2 OR N1L2)
= 1 - [P(L1L2) + P(L1N2) + P(N1L2)]
= 1 - [(120/700)(119/699) + (120/700)(580/699) + (580)/700)(120/699)]
= 0.7 (approx)

Cheers,
Brent
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