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## #1 2013-06-21 06:55:33

Al-Allo
Member
Registered: 2012-08-23
Posts: 324

### Little question (Probability)

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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## #2 2013-06-21 07:04:26

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 106,389

### Re: Little question (Probability)

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.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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## #3 2013-06-21 07:14:25

Al-Allo
Member
Registered: 2012-08-23
Posts: 324

### Re: Little question (Probability)

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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## #4 2013-06-21 07:18:17

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 106,389

### Re: Little question (Probability)

Hi;

You are welcome.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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## #5 2013-06-21 07:27:01

Al-Allo
Member
Registered: 2012-08-23
Posts: 324

### Re: Little question (Probability)

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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## #6 2013-06-21 07:37:56

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 106,389

### Re: Little question (Probability)

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.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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## #7 2013-06-21 07:39:49

Al-Allo
Member
Registered: 2012-08-23
Posts: 324

### Re: Little question (Probability)

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

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## #8 2013-06-21 07:40:36

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 106,389

### Re: Little question (Probability)

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

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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## #9 2013-06-21 07:44:11

Al-Allo
Member
Registered: 2012-08-23
Posts: 324

### Re: Little question (Probability)

Yes, so we can get to 0.

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## #10 2013-06-21 07:48:23

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 106,389

### Re: Little question (Probability)

Two person hitting is .32

Is that what you got?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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## #11 2013-06-21 07:52:31

Al-Allo
Member
Registered: 2012-08-23
Posts: 324

### Re: Little question (Probability)

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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## #12 2013-06-21 07:54:31

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 106,389

### Re: Little question (Probability)

Yes, you are correct?

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

Do you should see why that is wrong though?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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## #13 2013-06-21 07:57:23

Al-Allo
Member
Registered: 2012-08-23
Posts: 324

### Re: Little question (Probability)

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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## #14 2013-06-21 08:16:25

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 106,389

### Re: Little question (Probability)

Is this the answer you were expecting?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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## #15 2013-06-21 08:17:33

Al-Allo
Member
Registered: 2012-08-23
Posts: 324

### Re: Little question (Probability)

Which one ? The 0,14 ?

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## #16 2013-06-21 08:19:31

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 106,389

### Re: Little question (Probability)

Yes. That will make a good choice.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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## #17 2013-06-21 08:21:27

Al-Allo
Member
Registered: 2012-08-23
Posts: 324

### Re: Little question (Probability)

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

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## #18 2013-06-21 08:24:51

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 106,389

### Re: Little question (Probability)

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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## #19 2013-06-21 08:27:36

Al-Allo
Member
Registered: 2012-08-23
Posts: 324

### Re: Little question (Probability)

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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## #20 2013-06-21 08:31:32

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 106,389

### Re: Little question (Probability)

I got two different answers when I treed it.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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## #21 2013-06-21 08:31:58

Al-Allo
Member
Registered: 2012-08-23
Posts: 324

### Re: Little question (Probability)

... What are those answers ?

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## #22 2013-06-21 08:34:48

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 106,389

### Re: Little question (Probability)

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

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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## #23 2013-06-21 08:36:06

Al-Allo
Member
Registered: 2012-08-23
Posts: 324

### Re: Little question (Probability)

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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## #24 2013-06-21 08:38:13

Al-Allo
Member
Registered: 2012-08-23
Posts: 324

### Re: Little question (Probability)

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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## #25 2013-06-21 08:43:18

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 106,389

### Re: Little question (Probability)

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

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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