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# Twenty-five percent of a group of students are

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Senior Manager
Joined: 27 Feb 2014
Posts: 349
Location: India
GMAT 1: 570 Q49 V20
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Twenty-five percent of a group of students are  [#permalink]

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Updated on: 10 Feb 2020, 02:03
1
2
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Difficulty:

45% (medium)

Question Stats:

63% (01:44) correct 37% (01:32) wrong based on 38 sessions

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Twenty-five percent of a group of students are exactly 10 years old. The students are asked one at a time their age. What is the probability that the 5th student asked is the first exactly 10 years old?

a. $$\frac{1}{4^5}$$

b. $$\frac{3^5}{4^5}$$

c. $$\frac{3^4}{4^5}$$

d. $$\frac{1}{4^4}$$*$$\frac{3}{4}$$

e. Cannot be determined

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Originally posted by kapil1 on 04 Feb 2020, 02:55.
Last edited by kapil1 on 10 Feb 2020, 02:03, edited 1 time in total.
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Re: Twenty-five percent of a group of students are  [#permalink]

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04 Feb 2020, 07:30
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The probability that the 5th student is the first 10 year old is the same as the probably that the first four are NOT 10 times the probability that the 5th is 10.

If 25% are 10, then 75% are not, so (3/4)^4 * 1/4 is the probability that the first four are not 10, and the 5th is 10

ANS) C
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Re: Twenty-five percent of a group of students are  [#permalink]

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06 Feb 2020, 04:21
Bunuel , I chose Answer E (cannot be determined) because I thought this exercise was "without replacement": Once you have picked the first student out of n students, you have n-1 students left to ask their age. Can you help explain why this is wrong? Thanks!
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Re: Twenty-five percent of a group of students are  [#permalink]

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08 Feb 2020, 19:22
1
kapil1 wrote:
Twenty-five percent of a group of students are exactly 10 years old. The students are asked one at a time their age. What is the probability that the 5th student asked is the first exactly 10 years old?

a. $$\frac{1}{4^5}$$
b. $$\frac{3^5}{4^5}$$
c. $$\frac{3^4}{4^5}$$
d. $$\frac{1}{4^4}$$*$$\frac{3}{4}$$
e. Cannot be determined

We can let Y = 10 years old and N = not 10 years old, so we need the probability of NNNNY, which is:

(3/4)^4 x 1/4 = (3^4) / (4^5)

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Re: Twenty-five percent of a group of students are   [#permalink] 08 Feb 2020, 19:22
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