Probability-GFG

Question

In a bunch of $13$ T-shirts only $1$ is of Medium size, which is correct fit for the searching person.

Each time wrong size is picked, the person throws it away and pick the next T-shirt.

What is the probability that the correct size T-shirt can be searched in $8^{th}$ attempt ?

My attempt : $\frac{1}{13}$ where i went wrong ?

Comments

@ srestha How $1/8$ could you please explain?

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like this

choose anyone of 13 t-shirt first

then anyone of 12 t-shirt

then any one of 11

...............

u r throwing out t shirt, so t shirt cannot repeat

So, in it is 8th attempt

u just choose 1 tshirt

what is ans?? any explaination given?

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But one out of 13 is probability of what? Choosing correct one will be 1/13 and choosing wrong one will be 12/13. Correct tshirt should be at 8th attempt

Answer 1

Let L_i be the event of searching medium sized T-shirt in i^th attempt. P(L'₁ ∩ L'₂ ∩ L'₃ ∩ L'₄ ∩ L'₅ ∩ L'₆ ∩ L'₇ ∩ L₈ ) = P(L'₁) . P(L'₂ / L'₁) . P(L'₃ / L'₁ ∩ L'₂) ------- P( L₈ / L'₁ ∩ L'₂ ...... L'₇) = 8/13 . 7/12. 6/11. 5/10. 4/9. 3/8. 2/7. 1/6 = 40320 / 51891840 = 1 / 1287.... answer given was this how can this be the answer

Comments

why u chooses 8/13 first??

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COPIED FROM GEEKSFORGEEKS...

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KUCH BHI..???

Answer 2

The question and the answer are both a bit clumsy here.

They are saying, than the T-shirt can be found in eighth attempt. No one knows if they wanna say, 

• The selection process puts the shirts into a random order, and we have a "success" if the shirt is in any of the first eight positions (first interpretation).
• Or under the assumption that "success" means finding the medium shirt only on the eighth attempt, not earlier.

The word CAN here doesn't signifies surety.

The proposed solution on the website makes the absurd claim that the probability not to find a medium shirt on the first attempt is 8/13. That would be the correct probability if the problem statement said there were five medium shirts, but the problem statement clearly says there is only one. Hence the correct probability is 12/13. The remaining probabilities are as 11/12 * 10/11* 9/10....and so on.

(Under the assumption that "success" means finding the medium shirt only on the eighth attempt, not earlier)  the probability to be in the eighth position is 1/13

Now, by directly computing P(L′1∩L′2∩L′3∩L′4∩L′5∩L′6∩L′7∩L8) as proposed in the solution on the website,  it is attributable to the fact that we computed the probabilities correctly and they gave the wrong probabilities. You need only make the obvious cancellations in order to obtain a simple fraction as the solution.

Still we can't give a correct solution to an incorrect question.  So I guess, everyone's assumption would be right here. And marks should be given to all.

Answer 3

Here,we are given 13 shirts and the man throws them one by one if they do not fit.

So,we can do this by binomial distribution.

n=8 ( no of trials)

 

x=1( no of times the trial needs to get succeeded i.e if 1 shirt fits then work is done )

 

p=probability of success = 1/8 , since we are doing it for 8 attempts so total no of shirts that would be taken into account are 8

 

q = probability of failure= 7/8, since only 1 shirt which is medium size will fit

 

put them in formula i.e (nCx *p^x*q^n-x)

 

therefore I think the answer is 0.39 which is

 

5/13.