# Thread: Probability using tree diagrams

1. ## 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

2. ## 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.

3. ## 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

4. ## Re: Probability using tree diagrams

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.

5. ## 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

6. ## Re: Probability using tree diagrams

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).