Probability / Statistics - Event Occurring Only Once












-1















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







share|improve this question























  • 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
















-1















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







share|improve this question























  • 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














-1












-1








-1








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







share|improve this question














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






share|improve this question













share|improve this question











share|improve this question




share|improve this question










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



















  • 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












2 Answers
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1














You have three possible favorable paths:




  1. Win first race and lose the next two, with probability (1/10)x(9/10)x(9/10)

  2. Lose first one, win second one and lose also third one, with probability (9/10)x(1/10)x(9/10)

  3. 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






share|improve this answer
























  • 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



















1














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.)






share|improve this answer
























  • 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












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2 Answers
2






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2 Answers
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active

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1














You have three possible favorable paths:




  1. Win first race and lose the next two, with probability (1/10)x(9/10)x(9/10)

  2. Lose first one, win second one and lose also third one, with probability (9/10)x(1/10)x(9/10)

  3. 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






share|improve this answer
























  • 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
















1














You have three possible favorable paths:




  1. Win first race and lose the next two, with probability (1/10)x(9/10)x(9/10)

  2. Lose first one, win second one and lose also third one, with probability (9/10)x(1/10)x(9/10)

  3. 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






share|improve this answer
























  • 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














1












1








1







You have three possible favorable paths:




  1. Win first race and lose the next two, with probability (1/10)x(9/10)x(9/10)

  2. Lose first one, win second one and lose also third one, with probability (9/10)x(1/10)x(9/10)

  3. 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






share|improve this answer













You have three possible favorable paths:




  1. Win first race and lose the next two, with probability (1/10)x(9/10)x(9/10)

  2. Lose first one, win second one and lose also third one, with probability (9/10)x(1/10)x(9/10)

  3. 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







share|improve this answer












share|improve this answer



share|improve this answer










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



















  • 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













1














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.)






share|improve this answer
























  • 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
















1














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.)






share|improve this answer
























  • 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














1












1








1







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.)






share|improve this answer













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.)







share|improve this answer












share|improve this answer



share|improve this answer










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



















  • 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


















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