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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

Hi, I need someone to help me make sense of something :

We have three person shooting one arrow.

P(Thomas hits the target) = 0,4 >> 0,6 (He doesn't hit it)

P(Alicia hits the target) = 0,3 >> 0,7

P(Julie hits the target)= 0,8 >> 0,2

Now, the question is : What is the probability of atleast one person out of the three hits the target if they shoot one arrow each.

A' = No one hitting the target

0,6 * 0,7 * 0,2 = 0,084 or 8,4 %

Now, we know that :

A = Atleast one person hitting the target

1- 0,084 = 0,916 or 91,6%

There is one LITTLE thing which I do not understand ! It concerns the A, what does the 91,6 % stand for ? Yes, it's said to be " Atleast one person hitting the target" But I don't understand why. How can you substract the probability of no one getting the target and get the probability of atleast one person hitting it ? I feel it doesn't have any link together ? COuld someone enlighten me to see how it's possible ? Thank you ( If you do not understand what I mean, I will reformulate )

*Last edited by Al-Allo (2013-06-21 06:55:53)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Hi;

How can you substract the probability of no one getting the target and get the probability of atleast one person hitting it ?

At least one person hitting the target means 1, 2 or all 3.

There are only these possibilities

1) No one hits

2) 1 person hits

3) 2 persons hit

4) 3 persons hit

At least one person hitting the target is 2) + 3) + 4)

From the laws of probability.

1) + 2) + 3) + 4) = 1

You calculated 1) to be .084

.084 +2) + 3) + 4) = 1

subtract .084 from both sides

2) + 3) + 4) = .916

And you know what 2) + 3) + 4) is by now.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

AHHHHHHH.. Thank you. THe problem was, I wasn't sure that atleast one person would also mean all the three like you showed me(It didn't make sense that it would mean ONLY one person, this is why I asked the question about it). A vocabulary problem ?

Anyway, thank you very much ! Im happy that I can count on this forum my problems

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Hi;

You are welcome.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

Also, would this be corrrect :

1-0,084 = 0,916

0,916- 0,096 = 0,82 0,096(all the 3 hitting) = 0,4*0,3*0,8

Two person hitting = 0,4 * 0,3= 0,12 or 0,4*0,8= 0,32 or 0,3*0,8=0,24

0,12+0,32+0,24= 0,68

0,82-0,68=0,14

Is this any good ?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

You have .096 for all three that is correct.

You have .084 for none hitting.

What are you now looking for?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

I'm trying to get to 0 by substracting every probability. To be able to see in depth ^^

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

You want probability that only one hits and probability that just 2 hit?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

Yes, so we can get to 0.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Two person hitting is .32

Is that what you got?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

Well, I got three of them

Two person hitting : 0,4 * 0,3= 0,12 or 0,4*0,8= 0,32 or 0,3*0,8=0,24

0,12+0,32+0,24= 0,68

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Yes, you are correct?

Now how do you get the last one.Just one hit

Do you should see why that is wrong though?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

Here's what I did :

0,82-0,68=0,14

and 0,14-0,14= 0

0,14, the probability of only one person hitting the target

Is there any corrections to be made ? Thanks

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Is this the answer you were expecting?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

Which one ? The 0,14 ?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Yes. That will make a good choice.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

Well, I don't see what else it could be.... So...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Okay, I thought you had the answer already.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

Ah, no I don't, I only had to find the probability of atleast 1 person hitting the target. But would the 0,14 that only one person hits the target be good, would it be the answer you would have chosen ?

*Last edited by Al-Allo (2013-06-21 08:27:59)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

I got two different answers when I treed it.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

... What are those answers ?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

For any 2 hitting the target .392 and for 1 hitting the target .428

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

Well, here's how I see it :

If 1 is our omega, the we SHOULD get this :

14% (Only one person) + 68 % (Only two persons, with the different variations of the two persons, because this is omega) + 9,6 % (The three of them hitting) + 8,4 % (none hitting) = 100 %

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

bobbym wrote:

For any 2 hitting the target .392 and for 1 hitting the target .428

How did you get .392 ? Here's how I got for any two : 0,4 * 0,3= 0,12 or 0,4*0,8= 0,32 or 0,3*0,8=0,24

Could you show me ?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

That is what you are doing wrong you are only firing two arrows for each one. But the problem fires 3 arrows!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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