# Math question

Can you please tell me why the calculations are wrong?

CORRECT ANSWER IS B

The 1st person can pick anyone. the remaining 3 must each pick the same person, with Pr = 1/5,
thus by the multiplicative principle,
indicated Pr = (1/5)³ = 1/125= 0.008000
Asked:
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Senior .Net DeveloperCommented:
you're ignoring the first choice.

it's pr (1/5) ^ 4

Simplify it down to two witnesses.

By your logic the first one chooses anyone, and it's only the second guy that counts.

Not the case.

It's the probability that the first guy picks the person AND the second guy picks the same person.  (1/5 * 1/5)
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Commented:
This is another horrible ambiguous question:
Does "same person" in the last sentence refer to "same man" in the first sentence?

Ignore the first part of the problem.  Each of 4 witnesses has a choice of 5 suspects.
So there are 54 = 625 possible ways for them to vote.

In 5 of those cases they will be voting for the same person.  There is really no other way to phrase it.
And so the probability of this happening is   5/625  =  1/125  =  0.008
2

Commented:
I like d-glitch's response, and I was puzzled at first at the Answer B.

But then I had to think about the practical nature of lineups where my total understanding comes from watching TV shows. In every TV show I watched where there is a lineup of 5 men, the detectives believe there is one person that committed the crime. Call him person A. In other words, in the practical nature of a lineup, the same man refers to a specific man that the detectives had in mind.

Then the 4 witnesses vote (in our example, randomly). As d-glitch said, there are 5^4 = 625 possible ways for them to vote. But only in one case will they have all voted for man A. And that leads to an answer of 1/625 = 0.0016.

I reluctantly have to agree with the Answer B.
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