Math Is Fun Forum

Dharshi

Member

Registered: 2006-10-31

Posts: 56

Statistical problem

Hey,... i need help with this problem.

On the basis of information it is known that the judgement given by the judge is correct in 90 percent of the cases. Also let us suppose that 40 percent of the cirminals produced befoer court are actually innocent. Find the probability of the event that an innocent person produced before the court have been declared innocent.

Can anyone  help me with this problem ?the answer in the book is 0.857.
I tried it but i didnt get that answer.:(

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Statistical problem

The wording of the question is a bit misleading. It's telling you that a person has been declared innocent, and then wants to know the probability that they actually were innocent.

There are two ways for a person to be declared innocent:
- They are innocent and are declared so correctly.
- They are guilty but are incorrectly declared innocent.

The probability of the first event is P(innocent) x P(correct declare) = 0.4 x 0.9 = 0.36
Similarly, the probability of the second event is 0.6 x 0.1 = 0.06

So the total probability of someone being declared innocent is 0.36 + 0.06 = 0.42.

Hence, the probability of someone being innocent, given that they are declared innocent, is 0.36/0.42 = 6/7 ≈ 0.857

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Why did the vector cross the road?
It wanted to be normal.

Dharshi

Member

Registered: 2006-10-31

Posts: 56

Re: Statistical problem

hi,

thanks a lot. i got it