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The retirement plan for a company allows employees to invest

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The retirement plan for a company allows employees to invest [#permalink] New post   09 May 2019, 01:37
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The retirement plan for a company allows employees to invest in 10 different mutual funds. Six of the 10 funds grew by at least 10% over the last year. If Sam randomly selected 4 of the 10 funds, what is the probability that at least 3 of Sam’s 4 funds grew by at least 10% over the last year?

(A) \(\frac{6C_3}{10C_4}\)

(B) \(\frac{6C_3*4C_1}{10C_4}\)

(C) \(\frac{6C_3*4C_1+6C_4}{10P_4}\)

(D) \(\frac{6P_3*4P_1}{10C_4}\)

(E) \(\frac{6C_3*4C_1 + 6C_4}{10C_4}\)
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Re: The retirement plan for a company allows employees to invest [#permalink] New post   10 May 2019, 02:14
There are 10 mutual funds.
6 of them grew by at least 10% and 4 that didn't grew by at least 10%
Sam picks 4 fund type.

So the sample space is 10c4. Hence we can eliminate option c.
Now this is a combination problem as we don't have to consider order of choice. Therefore we can also get rid of option D.
The successful option is given by 6c3*4c1 + 6c4. This expression should appear in the numerator of options. Therefore the ans is E.
Here, Sam can chose either 3 funds that grew by atleast 10% and 1 that didn't or he can chose all 4 funds that grew by 10%.
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Re: The retirement plan for a company allows employees to invest [#permalink] New post   28 Aug 2019, 02:06
This is a very nice question. Thanks!
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Re: The retirement plan for a company allows employees to invest [#permalink] New post   10 Feb 2020, 20:29
Carcass wrote:
The retirement plan for a company allows employees to invest in 10 different mutual funds. Six of the 10 funds grew by at least 10% over the last year. If Sam randomly selected 4 of the 10 funds, what is the probability that at least 3 of Sam’s 4 funds grew by at least 10% over the last year?

(A) \(\frac{6C_3}{10C_4}\)

(B) \(\frac{6C_3*4C_1}{10C_4}\)

(C) \(\frac{6C_3*4C_1+6C_4}{10P_4}\)

(D) \(\frac{6P_3*4P_1}{10C_4}\)

(E) \(\frac{6C_3*4C_1 + 6C_4}{10C_4}\)



There are 6 winning funds that grew more than 10%, and 4 losing funds that grew less than 10%.

The problem can be split into 3 sub-problems:

1) Sam has to choose 3 winning funds. This can be done in \(6C_3\) ways.

2) Sam has to choose 1 losing fund. This can be done in \(4C_1\) ways.

3) Sam has to choose all 4 funds to be winning funds. This can be done in \(6C_4\) ways.

This is how Sam chooses at least 3 winning funds. Hence, the total number of ways of choosing at least 3 winning funds is \(6C_3\)*\(4C_1\) + \(6C_4\)

If there were no restrictions (such as choosing at least 3 winning funds), Sam would have chosen funds in \(10C_4\) ways.

Hence, the probability that at least 3 of Sam’s 4 funds grew by at least 10% over the last year is \(\frac{6C_3*4C_1 + 6C_4}{10C_4}\)
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Re: The retirement plan for a company allows employees to invest [#permalink] New post   01 Mar 2022, 01:07
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The retirement plan for a company allows employees to invest [#permalink]
01 Mar 2022, 01:07
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