Two Plus Two Publishing LLC Two Plus Two Publishing LLC
 

Go Back   Two Plus Two Poker Forums > >

Notices

Probability Discussions of probability theory

Reply
 
Thread Tools Display Modes
Old 09-30-2017, 01:26 AM   #1
dan233
adept
 
dan233's Avatar
 
Join Date: Oct 2009
Posts: 861
Probability of getting award A or B

Hi
I have a 50% probability of getting award A and a 50% probability of getting award B.
What's the probablity of me getting either A or B?

Thanks
dan233 is offline   Reply With Quote
Old 09-30-2017, 04:43 AM   #2
dan233
adept
 
dan233's Avatar
 
Join Date: Oct 2009
Posts: 861
Re: Probability of getting award A or B

It is just 50%.. right?
dan233 is offline   Reply With Quote
Old 09-30-2017, 08:55 AM   #3
NewOldGuy
Pooh-Bah
 
Join Date: Mar 2009
Location: In the wires
Posts: 5,019
Re: Probability of getting award A or B

100%. Is this a joke or did you misstate the question? You have described a coin flip.
NewOldGuy is offline   Reply With Quote
Old 09-30-2017, 11:23 AM   #4
Lego05
Carpal \'Tunnel
 
Join Date: Mar 2006
Posts: 23,756
Re: Probability of getting award A or B

Are the awards determined independently? Or do they each happen at a 50% probability on the same trial such that if one does not happen, then the other must happen?

1. If the Awards are NOT independent, such that you mean the question like flip a coin and if it is heads, then get Award A and if it is tails, then get Award B, then there is a 50% chance of getting each award and a 100% chance of getting either award.

2. If the awards are independent (like flip 2 different coins, one to determine each), then:

.....(a) The chance of getting neither award is 0.5 * 0.5 = 0.25 = 25%, so, therefore, the chance to get at least one award is 1 - 0.25 = 0.75 = 75%.

.....(b) The chance to win exactly one award is 50%:

............(i) 0.5 (win Award A) * 0.5 (lose Award B) = 0.25
................0.5 (win Award B) * 0.5 (lose Award A) = 0.25
................0.25 + 0.25 = 0.5 = 50%

...........OR

............(ii) Win Both Awards = 0.5 * 0.5 = 0.25 = 25%
.................Lose Both Awards = 0.5 * 0.5 = 0.25 = 25%
.................Win Exactly One Award = 1 - 0.25 - 0.25 = 0.5 = 50%

Last edited by Lego05; 09-30-2017 at 11:30 AM.
Lego05 is offline   Reply With Quote
Old 09-30-2017, 11:31 AM   #5
statmanhal
Pooh-Bah
 
Join Date: Jan 2009
Posts: 3,968
Re: Probability of getting award A or B

Assume the awards are not mutually exclusive (you can get both)

A: Guess right heads or tails with a penny toss
B. Guess right heads or tails with a nickel toss

Let a = P(A award) = 0.50, b = P(B award) = 0.50.

1. P(A only) = a AND not b = 0.5 * 0.5 = 0.25
2. P(B only) = not a AND b = 0.5 * 0.5 0.25
3. P(A and B) = a AND b = 0.5 * 0.5 = 0.25
4. P(neither A or B) = not a AND not b = 0.5 *0.5 = 0.25

Note: 1.+2.+3. +4.=1.0 (=all possibilities)

5. P(A or B but not both) = a only + b only = 1. + 2. = 0.50
6. P(A or B or both) = a only + b only + a AND b = .1.+2.+3 = 0.25 + 0.25+ 0.25 = 0.75

Edit: Didn't see Lego's response but I'll leave this up as it shows a slightly different way of showing all possibilities.
statmanhal is offline   Reply With Quote
Old 09-30-2017, 11:50 AM   #6
dan233
adept
 
dan233's Avatar
 
Join Date: Oct 2009
Posts: 861
Re: Probability of getting award A or B

Quote:
Originally Posted by NewOldGuy View Post
100%. Is this a joke or did you misstate the question? You have described a coin flip.
Not a joke. And not a coinflip
dan233 is offline   Reply With Quote
Old 09-30-2017, 12:07 PM   #7
dan233
adept
 
dan233's Avatar
 
Join Date: Oct 2009
Posts: 861
Re: Probability of getting award A or B

Lego05 and statmanhal.
Thanks for your replies.
Makes perfect sense
dan233 is offline   Reply With Quote
Old 09-30-2017, 12:46 PM   #8
NewOldGuy
Pooh-Bah
 
Join Date: Mar 2009
Location: In the wires
Posts: 5,019
Re: Probability of getting award A or B

Quote:
Originally Posted by dan233 View Post
Not a joke. And not a coinflip
Sorry I just assumed you meant mutually exclusive.
NewOldGuy is offline   Reply With Quote
Old 10-01-2017, 03:06 PM   #9
dan233
adept
 
dan233's Avatar
 
Join Date: Oct 2009
Posts: 861
Re: Probability of getting award A or B

If the probability of getting award A is 16%, 24% to get award B and probability of getting both A and B is 11%,
what is the probability of getting at least one award?


Thanks
dan233 is offline   Reply With Quote
Old 10-01-2017, 04:33 PM   #10
NewOldGuy
Pooh-Bah
 
Join Date: Mar 2009
Location: In the wires
Posts: 5,019
Re: Probability of getting award A or B

Quote:
Originally Posted by dan233 View Post
If the probability of getting award A is 16%, 24% to get award B and probability of getting both A and B is 11%,
what is the probability of getting at least one award?


Thanks
These figures would mean they are not independent, so we need to know the relationship and the selection method. If they were independent then the probability of both is A * B, not 11%.
NewOldGuy is offline   Reply With Quote
Old 10-01-2017, 04:49 PM   #11
dan233
adept
 
dan233's Avatar
 
Join Date: Oct 2009
Posts: 861
Re: Probability of getting award A or B

Quote:
Originally Posted by NewOldGuy View Post
These figures would mean they are not independent, so we need to know the relationship and the selection method. If they were independent then the probability of both is A * B, not 11%.
Well, can we just imagine that the probabilities of getting award A is 16%, 24% for B, but due to irrational psychological factors (for example), the probability of a jury granting both awards is 11%?

Last edited by dan233; 10-01-2017 at 04:54 PM.
dan233 is offline   Reply With Quote
Old 10-01-2017, 06:31 PM   #12
NewOldGuy
Pooh-Bah
 
Join Date: Mar 2009
Location: In the wires
Posts: 5,019
Re: Probability of getting award A or B

Quote:
Originally Posted by dan233 View Post
Well, can we just imagine that the probabilities of getting award A is 16%, 24% for B, but due to irrational psychological factors (for example), the probability of a jury granting both awards is 11%?
Sure, but that makes them not independent. So I don't think your question can be answered without knowing the relationship and how they affect each other. The cases are A not B, B not A, neither, and both. We don't know the first two of those (and I'm not sure we know the neither case).

Last edited by NewOldGuy; 10-01-2017 at 06:37 PM.
NewOldGuy is offline   Reply With Quote
Old 10-02-2017, 12:47 AM   #13
nickthegeek
centurion
 
Join Date: Sep 2011
Posts: 189
Re: Probability of getting award A or B

Quote:
Originally Posted by dan233 View Post
If the probability of getting award A is 16%, 24% to get award B and probability of getting both A and B is 11%,
what is the probability of getting at least one award?
Just use the inclusion-exclusion principle:

P(A OR B) = P(A) + P(B) - P(A AND B)
nickthegeek is offline   Reply With Quote
Old 10-02-2017, 12:55 AM   #14
nickthegeek
centurion
 
Join Date: Sep 2011
Posts: 189
Re: Probability of getting award A or B

Quote:
Originally Posted by NewOldGuy View Post
The cases are A not B, B not A, neither, and both. We don't know the first two of those (and I'm not sure we know the neither case).
Actually, we know all the four quantities above and it should pretty obvious how to calculate them. If we win A 16% of the times and we win both A and B 11% of the times, we obviously win A but not B 5% of the times. Also without having knowledge of the inclusion-exclusion principle, it should be obvious that:

P(A OR B) = P(A NOT B) + P(B NOT A) + P(A AND B)

which reduces to the formula I gave above.
nickthegeek is offline   Reply With Quote
Old 10-02-2017, 04:25 AM   #15
dan233
adept
 
dan233's Avatar
 
Join Date: Oct 2009
Posts: 861
Re: Probability of getting award A or B

Quote:
Originally Posted by nickthegeek View Post
Just use the inclusion-exclusion principle:

P(A OR B) = P(A) + P(B) - P(A AND B)
Hi
Thanks for you reply
A question:
Doesnt the above calculation remove the case where you get both A&B?
A&B should be included when the question is "At least" meaning= A or B or A&B
dan233 is offline   Reply With Quote
Old 10-02-2017, 06:42 AM   #16
nickthegeek
centurion
 
Join Date: Sep 2011
Posts: 189
Re: Probability of getting award A or B

No, doesn't remove the case, since P(A) + P(B) double counts the time where you win both A and B.

However, imagine this equivalent problem. There are 100 people in a room. 16 of them have the object A. 24 have the object B. 11 have both objects.

How many have the object A, but don't have B?
How many have the object A, but don't have B?
How many have at least one of them?
How many have none of them?

These are trivial questions. However, let's see them.

- Since 16 people have A and 11 of them have both A and B, we are left with just 5 people with only A.
- At the same way, we have 24-11=13 people having B but not A
- Finally, we have 5 people with A but not B, 13 people with B but not A and 11 people with both of them -> 29 people with at least A or B.
- 71 people have nothing.

See where IEP comes from? When we add 15+24 we count the guys that have both A and B twice since they belong to both the 15 and the 24. So we have to subtract them to have the guys having at least one of them.
nickthegeek is offline   Reply With Quote
Old 10-02-2017, 07:31 AM   #17
NewOldGuy
Pooh-Bah
 
Join Date: Mar 2009
Location: In the wires
Posts: 5,019
Re: Probability of getting award A or B

Quote:
Originally Posted by nickthegeek View Post
Actually, we know all the four quantities above and it should pretty obvious how to calculate them. If we win A 16% of the times and we win both A and B 11% of the times, we obviously win A but not B 5% of the times. Also without having knowledge of the inclusion-exclusion principle, it should be obvious that:

P(A OR B) = P(A NOT B) + P(B NOT A) + P(A AND B)

which reduces to the formula I gave above.
Thanks, I see now.
NewOldGuy is offline   Reply With Quote
Old 10-02-2017, 09:47 PM   #18
dan233
adept
 
dan233's Avatar
 
Join Date: Oct 2009
Posts: 861
Re: Probability of getting award A or B

Nickthegeek
Ok so -P(A and B) just sets the degree to which A and B are overlapping (in a Venn diagram). It doesnt remove it.

Thanks
dan233 is offline   Reply With Quote
Old 10-03-2017, 08:32 AM   #19
heehaww
Pooh-Bah
 
heehaww's Avatar
 
Join Date: Aug 2011
Location: It was an attractive goat in AR
Posts: 4,193
Re: Probability of getting award A or B

It doesn't "set the degree" of anything, it makes you not count the overlapping region more than once.

If you flip a coin twice, the chance of at least one Tails is not 100%, it's (50+50-25)%. The overlap is 25%, which gets counted twice if you don't subtract it. Alternatively, you don't need to subtract anything if you add each region separately (but it's often easier to over-add and then subtract).
heehaww is offline   Reply With Quote
Old 10-03-2017, 01:58 PM   #20
dan233
adept
 
dan233's Avatar
 
Join Date: Oct 2009
Posts: 861
Re: Probability of getting award A or B

Quote:
Originally Posted by nickthegeek View Post
Actually, we know all the four quantities above and it should pretty obvious how to calculate them. If we win A 16% of the times and we win both A and B 11% of the times, we obviously win A but not B 5% of the times. Also without having knowledge of the inclusion-exclusion principle, it should be obvious that:

P(A OR B) = P(A NOT B) + P(B NOT A) + P(A AND B)

which reduces to the formula I gave above.
Thanks

Last edited by dan233; 10-03-2017 at 02:23 PM.
dan233 is offline   Reply With Quote

Reply
      

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off


Forum Jump


All times are GMT -4. The time now is 11:48 AM.


Powered by vBulletin®
Copyright ©2000 - 2017, Jelsoft Enterprises Ltd.
Copyright © 2008-2010, Two Plus Two Interactive
 
 
Poker Players - Streaming Live Online