# Probability using tree diagrams

• Jul 6th 2011, 08:48 PM
MathsBeforeBedtime
Probability using tree diagrams
Hi there, I'm not sure if this question is WITH replacement or WITHOUT replacement. I tried it both ways and didn't come to the correct answer. I'm assuming this question makes more sense WITHOUT replacement.

Question:
http://i.imgur.com/nfBSA.png
• Jul 7th 2011, 02:44 AM
e^(i*pi)
Re: Probability using tree diagrams
Without replacement makes more sense to me, why would you replace a car that is known (not) to work?

What have you tried as to solving the question?

On a tree diagram you multiply along the branches and add down the branches.
• Jul 7th 2011, 03:28 AM
MathsBeforeBedtime
Re: Probability using tree diagrams
Yes I know this. I did Faulty and not faulty.

{Faulty = 3 / 100 Not Faulty = 97/100} - first branch
{(Faulty = 2 / 99 and Not Faulty = 97/99) comes off the Faulty branch, (Faulty = 3 / 99, Not Faulty = 96 / 99) comes off the not faulty branch} - Second branch
{(Faulty = 1 / 98 and Not Faulty = 97/98) comes off the first Faulty branch and second faulty branch...Etc Think you'll understand what I mean} - Third branch

I did P(1 is faulty) = (3/100*97/98*96/98) + (97/100*3/99*96/98) + (97/100*96/99*3/98) = 1164 / 13475

Correct answer: 84 681 / 1 000 000
• Jul 7th 2011, 03:48 AM
mr fantastic
Re: Probability using tree diagrams
Quote:

Originally Posted by MathsBeforeBedtime
Yes I know this. I did Faulty and not faulty.

{Faulty = 3 / 100 Not Faulty = 97/100} - first branch
{(Faulty = 2 / 99 and Not Faulty = 97/99) comes off the Faulty branch, (Faulty = 3 / 99, Not Faulty = 96 / 99) comes off the not faulty branch} - Second branch
{(Faulty = 1 / 98 and Not Faulty = 97/98) comes off the first Faulty branch and second faulty branch...Etc Think you'll understand what I mean} - Third branch

I did P(1 is faulty) = (3/100*97/98*96/98) + (97/100*3/99*96/98) + (97/100*96/99*3/98) = 1164 / 13475

Correct answer: 84 681 / 1 000 000

As far as I'm concerned, your answer is the correct one. The so-called correct answer is not correct.
• Jul 9th 2011, 04:41 AM
MathsBeforeBedtime
Re: Probability using tree diagrams
Turns out it is with replacement. P(1 is faulty)=3/100*97/100*97/100 *3 =84 681 / 1 000 000
• Jul 9th 2011, 04:24 PM
mr fantastic
Re: Probability using tree diagrams
Quote:

Originally Posted by MathsBeforeBedtime
Turns out it is with replacement. P(1 is faulty)=3/100*97/100*97/100 *3 =84 681 / 1 000 000

How ridiculous

1. Because this is not what would happen in the real world.

2. Because the question never makes it clear that it's the stupid interpretation that's required.

Whoever wrote the question should be shot (metaphorically, of course).