Probability / Statistics - Event Occurring Only Once
If I have a 1/10 chance of winning a race. What chance do I have of winning exactly one race if I take part in three separate races? My chances of winning are 1/10 for each race. I have been told the answer is 24.3% but I have no idea how this number was calculated no matter how hard I try. The closest I get is 27.1% which is 1 - (9/10)^3
statistics probability
asked Nov 22 '18 at 0:48
AzaAza
257
add a comment |
If I have a 1/10 chance of winning a race. What chance do I have of winning exactly one race if I take part in three separate races? My chances of winning are 1/10 for each race. I have been told the answer is 24.3% but I have no idea how this number was calculated no matter how hard I try. The closest I get is 27.1% which is 1 - (9/10)^3
statistics probability
asked Nov 22 '18 at 0:48
AzaAza
257
This may also be a helpful read, as this deals with a similar problem (and has that formula I was talking about): math.stackexchange.com/questions/684899/…
– kylew
Nov 22 '18 at 1:05
Thanks I found things like this last night but I struggled to understand these equations
– Aza
Nov 22 '18 at 1:16
I'm voting to close this question as off-topic because it's about probability / mathematics and not directly about programming / coding / software algorithms / programming tools.
– Pang
Dec 7 '18 at 1:12
add a comment |
If I have a 1/10 chance of winning a race. What chance do I have of winning exactly one race if I take part in three separate races? My chances of winning are 1/10 for each race. I have been told the answer is 24.3% but I have no idea how this number was calculated no matter how hard I try. The closest I get is 27.1% which is 1 - (9/10)^3
statistics probability
asked Nov 22 '18 at 0:48
AzaAza
257
If I have a 1/10 chance of winning a race. What chance do I have of winning exactly one race if I take part in three separate races? My chances of winning are 1/10 for each race. I have been told the answer is 24.3% but I have no idea how this number was calculated no matter how hard I try. The closest I get is 27.1% which is 1 - (9/10)^3
statistics probability
statistics probability
asked Nov 22 '18 at 0:48
AzaAza
257
asked Nov 22 '18 at 0:48
AzaAza
257
asked Nov 22 '18 at 0:48
AzaAza
257
asked Nov 22 '18 at 0:48
AzaAza
257
asked Nov 22 '18 at 0:48
AzaAza
257
257
This may also be a helpful read, as this deals with a similar problem (and has that formula I was talking about): math.stackexchange.com/questions/684899/…
– kylew
Nov 22 '18 at 1:05
Thanks I found things like this last night but I struggled to understand these equations
– Aza
Nov 22 '18 at 1:16
I'm voting to close this question as off-topic because it's about probability / mathematics and not directly about programming / coding / software algorithms / programming tools.
– Pang
Dec 7 '18 at 1:12
add a comment |
This may also be a helpful read, as this deals with a similar problem (and has that formula I was talking about): math.stackexchange.com/questions/684899/…
– kylew
Nov 22 '18 at 1:05
Thanks I found things like this last night but I struggled to understand these equations
– Aza
Nov 22 '18 at 1:16
I'm voting to close this question as off-topic because it's about probability / mathematics and not directly about programming / coding / software algorithms / programming tools.
– Pang
Dec 7 '18 at 1:12
This may also be a helpful read, as this deals with a similar problem (and has that formula I was talking about): math.stackexchange.com/questions/684899/…
– kylew
Nov 22 '18 at 1:05
This may also be a helpful read, as this deals with a similar problem (and has that formula I was talking about): math.stackexchange.com/questions/684899/…
– kylew
Nov 22 '18 at 1:05
Thanks I found things like this last night but I struggled to understand these equations
– Aza
Nov 22 '18 at 1:16
Thanks I found things like this last night but I struggled to understand these equations
– Aza
Nov 22 '18 at 1:16
I'm voting to close this question as off-topic because it's about probability / mathematics and not directly about programming / coding / software algorithms / programming tools.
– Pang
Dec 7 '18 at 1:12
I'm voting to close this question as off-topic because it's about probability / mathematics and not directly about programming / coding / software algorithms / programming tools.
– Pang
Dec 7 '18 at 1:12
add a comment |
2 Answers
2
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You have three possible favorable paths:
- Win first race and lose the next two, with probability (1/10)x(9/10)x(9/10)
- Lose first one, win second one and lose also third one, with probability (9/10)x(1/10)x(9/10)
- Lose first two and win third one, with probability (9/10)x(9/10)x(1/10)
Each favorable path has probability 81/1000. Adding them up, you get 243/1000=0.243
answered Nov 22 '18 at 1:00
DavidPMDavidPM
33529
Man I feel stupid now. I must have tried every other combination and got lost in the process. Thank you!
– Aza
Nov 22 '18 at 1:13
add a comment |
This isn't really the place to ask these kinds of questions, but in this case you could think of it as taking each of the different combinations (win-lose-lose, lose-win-lose, and lose-lose-win) and combining them like so: 0.1*0.9*0.9 + 0.9*0.1*0.9 + 0.9*0.9*0.1 (replace win with 0.1 or 1/10 and lose with 0.9, which is 1-0.1).
(By the way, there is a more general formula for this situation, but I can't remember it at the moment.)
answered Nov 22 '18 at 1:02
kylewkylew
15718
Thank you, I feel so stupid now. I placed the question in Quora first but answers are slow and I noticed other people had asked math questions on this platform previously. This will translate back into some code i'm writing
– Aza
Nov 22 '18 at 1:12
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
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active
oldest
votes
You have three possible favorable paths:
- Win first race and lose the next two, with probability (1/10)x(9/10)x(9/10)
- Lose first one, win second one and lose also third one, with probability (9/10)x(1/10)x(9/10)
- Lose first two and win third one, with probability (9/10)x(9/10)x(1/10)
Each favorable path has probability 81/1000. Adding them up, you get 243/1000=0.243
answered Nov 22 '18 at 1:00
DavidPMDavidPM
33529
Man I feel stupid now. I must have tried every other combination and got lost in the process. Thank you!
– Aza
Nov 22 '18 at 1:13
add a comment |
You have three possible favorable paths:
- Win first race and lose the next two, with probability (1/10)x(9/10)x(9/10)
- Lose first one, win second one and lose also third one, with probability (9/10)x(1/10)x(9/10)
- Lose first two and win third one, with probability (9/10)x(9/10)x(1/10)
Each favorable path has probability 81/1000. Adding them up, you get 243/1000=0.243
answered Nov 22 '18 at 1:00
DavidPMDavidPM
33529
Man I feel stupid now. I must have tried every other combination and got lost in the process. Thank you!
– Aza
Nov 22 '18 at 1:13
add a comment |
You have three possible favorable paths:
- Win first race and lose the next two, with probability (1/10)x(9/10)x(9/10)
- Lose first one, win second one and lose also third one, with probability (9/10)x(1/10)x(9/10)
- Lose first two and win third one, with probability (9/10)x(9/10)x(1/10)
Each favorable path has probability 81/1000. Adding them up, you get 243/1000=0.243
answered Nov 22 '18 at 1:00
DavidPMDavidPM
33529
You have three possible favorable paths:
- Win first race and lose the next two, with probability (1/10)x(9/10)x(9/10)
- Lose first one, win second one and lose also third one, with probability (9/10)x(1/10)x(9/10)
- Lose first two and win third one, with probability (9/10)x(9/10)x(1/10)
Each favorable path has probability 81/1000. Adding them up, you get 243/1000=0.243
answered Nov 22 '18 at 1:00
DavidPMDavidPM
33529
answered Nov 22 '18 at 1:00
DavidPMDavidPM
33529
answered Nov 22 '18 at 1:00
DavidPMDavidPM
33529
answered Nov 22 '18 at 1:00
DavidPMDavidPM
33529
33529
Man I feel stupid now. I must have tried every other combination and got lost in the process. Thank you!
– Aza
Nov 22 '18 at 1:13
add a comment |
Man I feel stupid now. I must have tried every other combination and got lost in the process. Thank you!
– Aza
Nov 22 '18 at 1:13
Man I feel stupid now. I must have tried every other combination and got lost in the process. Thank you!
– Aza
Nov 22 '18 at 1:13
Man I feel stupid now. I must have tried every other combination and got lost in the process. Thank you!
– Aza
Nov 22 '18 at 1:13
add a comment |
This isn't really the place to ask these kinds of questions, but in this case you could think of it as taking each of the different combinations (win-lose-lose, lose-win-lose, and lose-lose-win) and combining them like so: 0.1*0.9*0.9 + 0.9*0.1*0.9 + 0.9*0.9*0.1 (replace win with 0.1 or 1/10 and lose with 0.9, which is 1-0.1).
(By the way, there is a more general formula for this situation, but I can't remember it at the moment.)
answered Nov 22 '18 at 1:02
kylewkylew
15718
Thank you, I feel so stupid now. I placed the question in Quora first but answers are slow and I noticed other people had asked math questions on this platform previously. This will translate back into some code i'm writing
– Aza
Nov 22 '18 at 1:12
add a comment |
This isn't really the place to ask these kinds of questions, but in this case you could think of it as taking each of the different combinations (win-lose-lose, lose-win-lose, and lose-lose-win) and combining them like so: 0.1*0.9*0.9 + 0.9*0.1*0.9 + 0.9*0.9*0.1 (replace win with 0.1 or 1/10 and lose with 0.9, which is 1-0.1).
(By the way, there is a more general formula for this situation, but I can't remember it at the moment.)
answered Nov 22 '18 at 1:02
kylewkylew
15718
Thank you, I feel so stupid now. I placed the question in Quora first but answers are slow and I noticed other people had asked math questions on this platform previously. This will translate back into some code i'm writing
– Aza
Nov 22 '18 at 1:12
add a comment |
This isn't really the place to ask these kinds of questions, but in this case you could think of it as taking each of the different combinations (win-lose-lose, lose-win-lose, and lose-lose-win) and combining them like so: 0.1*0.9*0.9 + 0.9*0.1*0.9 + 0.9*0.9*0.1 (replace win with 0.1 or 1/10 and lose with 0.9, which is 1-0.1).
(By the way, there is a more general formula for this situation, but I can't remember it at the moment.)
answered Nov 22 '18 at 1:02
kylewkylew
15718
This isn't really the place to ask these kinds of questions, but in this case you could think of it as taking each of the different combinations (win-lose-lose, lose-win-lose, and lose-lose-win) and combining them like so: 0.1*0.9*0.9 + 0.9*0.1*0.9 + 0.9*0.9*0.1 (replace win with 0.1 or 1/10 and lose with 0.9, which is 1-0.1).
(By the way, there is a more general formula for this situation, but I can't remember it at the moment.)
answered Nov 22 '18 at 1:02
kylewkylew
15718
answered Nov 22 '18 at 1:02
kylewkylew
15718
answered Nov 22 '18 at 1:02
kylewkylew
15718
answered Nov 22 '18 at 1:02
kylewkylew
15718
15718
Thank you, I feel so stupid now. I placed the question in Quora first but answers are slow and I noticed other people had asked math questions on this platform previously. This will translate back into some code i'm writing
– Aza
Nov 22 '18 at 1:12
add a comment |
Thank you, I feel so stupid now. I placed the question in Quora first but answers are slow and I noticed other people had asked math questions on this platform previously. This will translate back into some code i'm writing
– Aza
Nov 22 '18 at 1:12
Thank you, I feel so stupid now. I placed the question in Quora first but answers are slow and I noticed other people had asked math questions on this platform previously. This will translate back into some code i'm writing
– Aza
Nov 22 '18 at 1:12
Thank you, I feel so stupid now. I placed the question in Quora first but answers are slow and I noticed other people had asked math questions on this platform previously. This will translate back into some code i'm writing
– Aza
Nov 22 '18 at 1:12
add a comment |
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This may also be a helpful read, as this deals with a similar problem (and has that formula I was talking about): math.stackexchange.com/questions/684899/…
– kylew
Nov 22 '18 at 1:05
Thanks I found things like this last night but I struggled to understand these equations
– Aza
Nov 22 '18 at 1:16
I'm voting to close this question as off-topic because it's about probability / mathematics and not directly about programming / coding / software algorithms / programming tools.
– Pang
Dec 7 '18 at 1:12