Twenty-five percent of a group of students are

Question

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

GMATSheep · Answer

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

quantrace · Answer

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!

ScottTargetTestPrep · Answer

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)

Answer: C

pratiksha1998 · Answer

Bunuel  Can you elaborate on this?

Twenty-five percent of a group of students are

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