Probability of this being a coincidence

[yay_math_000]

Someone sends an email to 5 people, one of which is me. They are claiming that they randomly selected 2 out of 5 of us for two different tasks. The two people that were supposedly randomly selected were the first two people listed on the email thread.

What is the probability that it is a coincidence that the two people listed first on the email thread were randomly chosen instead of intentionally selected?

 

[Deleted member 4993]

Someone sends an email to 5 people, one of which is me. They are claiming that they randomly selected 2 out of 5 of us for two different tasks. The two people that were supposedly randomly selected were the first two people listed on the email thread.

What is the probability that it is a coincidence that the two people listed first on the email thread were randomly chosen instead of intentionally selected?

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.

 

[yay_math_000]

I don't know where to start specifically on this. The two people that were listed first on the email thread have a union of probability out of a population of 5. Beyond that though I am not sure - how do you structure the probability after that? Is the email being sent one event, that has its own probability that then needs to be calculated against the second event, which is the selection of the 2 people out of 5?

 

[pka]

Someone sends an email to 5 people, one of which is me. They are claiming that they randomly selected 2 out of 5 of us for two different tasks. The two people that were supposedly randomly selected were the first two people listed on the email thread. What is the probability that it is a coincidence that the two people

If we choose two from five, that can be done in ten ways. That has nothing what-so-ever to do with order.

 

[yay_math_000]

If we choose two from five, that can be done in ten ways. That has nothing what-so-ever to due with order.

The order of the email recipients will reduce the probability of it being a coincidence.

If I take the union of P(A) and P(B), each with a probability of 20%, then the probability of both is 4%. Is that the right start for getting the solution?

 

[yay_math_000]

I neglected to include one detail. There were two emails. The first email was addressed to the 2 people out of 5, which were subsequently selected in a second email where they claimed that they used a random number generator to select 2 out of the 5 people for their tasks.
Does that reduce the probability?

 

[Dr.Peterson]

Someone sends an email to 5 people, one of which is me. They are claiming that they randomly selected 2 out of 5 of us for two different tasks. The two people that were supposedly randomly selected were the first two people listed on the email thread.

What is the probability that it is a coincidence that the two people listed first on the email thread were randomly chosen instead of intentionally selected?

Why couldn't they randomly select two people, and then put them first for whatever reason?

But I'll assume that it makes sense to ask for the probability that the first two people would be subsequently selected at random. There are C(5,2) = 10 ways to select two people, so the probability that those particular people would be selected is 1/10. That is low, but not unusually low. I don't think any crime can be proved.

If I take the union of P(A) and P(B), each with a probability of 20%, then the probability of both is 4%. Is that the right start for getting the solution?

No, that doesn't work. The two aren't selected independently. (If they were, then one could have been selected twice!) You don't really mean union, either.

Taking the approach you are trying, if A is "person A is chosen" and B is "person B is chosen", then

P(A and B are chosen) = P(A, then B) + P(B, then A) = P(A)*P(B|A) + P(B)*P(A|B) = (1/5)(1/4) + (1/5)(1/4) = 1/20 + 1/20 = 1/10.​