If one student is chosen randomly out of a group of seven students, th

Question

If one student is chosen randomly out of a group of seven students, then one student is again chosen randomly from the same group of seven, what is the probability that two different students will be chosen?

(A) 36/49
(B) 6/7
(C) 19/21
(D) 13/14
(E) 48/49

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Official Answer

B

(A) 36/49
(B) 6/7
(C) 19/21
(D) 13/14
(E) 48/49

Leon0973 · Answer

Easiest way to solve this is probably by reversing the question:

Instead of finding the probability of two different students being chosen, find the probability of the same student being chosen twice then subtract that answer from 1.

1/7 x 1/7 = 1/49

1 - 1/49 = 48/49

Answer choice E

Please correct me if I'm wrong.

EDIT

Forgot to take into account the probability that any of the 7 students could be selected.

Therefore, 7 x 1/49 = 7/49

1 - 7/49 = 42/49 = 6/7

imeanup · Answer

Probability of selecting 1 student =  \frac{1}{7} 
Probability of selecting the same student again =  \frac{1}{7} 
Total probability of this same student getting selected both times =  \frac{1}{7} * \frac{1}{7} 
= \frac{1}{49}

Probability P for all 7 students = 7* \frac{1}{49} = \frac{1}{7}

Probability of selecting 2 different student = 1 - P = 1- \frac{1}{7} 
 =  \frac{6}{7} 
 Ans B

TarunKumar1234 · Answer

P(One student is selected)= 1/7
P(In another selection, same student is selected)= 1 (because, we do have to select 1 out of 1 student)

And, P(Same student is selected)= 1/7 *1 = 1/7
Now, P(Same student is not selected)= 1-1/7= 6/7. B.

sekipap · Answer

First student selected has no probability attached: whatever student you pick, that's fine, so it is a certainty= 1
Second student is equal to the first with prob 1/7 and different with prob 6/7 
so answer= 6/7

Deyoz · Answer

Well i am not sure but i am 36 / 49 is the asnwer. my logic goes like this:

1. while choosing the first person, the probalibility is 1:
(7/7)
2. while choosing the second person, we are given a constraint that same the person is not allowed and hence the probability of not choosing the same person will be 1*6/7
3. Probability of choosing different person during second time selection will be 6/7
therefore, probability of choosing different person will be 1*6/7*6/7, giving 36/49.

please correct me if i am wrong!!

ShankSouljaBoi · Answer

7/7 * 6/7 = = 6/7.... B

TarunKumar1234 · Answer

Bunuel Let me know, my mistake to correct it.

ShankSouljaBoi · Answer

How is this E ?  chetansharma  ... since replacement is happening that means B should be it . Could you please provide a solution to this ?

chetan2u · Answer

Hi

It should be B. 
The first can be chosen in 7 ways, but the next has to be less the one chosen in first instance, so 6 ways. 
P=  \frac{7}{7}*\frac{6}{7}=\frac{6}{7}

Of course if replacement was not happening then surely the chosen person cannot be the same in both cases, so probability of both different will always be 1.

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