Odds of winning 1 out of 10 with 10% chance of one

jamesldavis1 said:

If there is a 10% chance of me winning say a tennis match, what would the chance be of me winning 1 match if I played 10 matches?

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Are you supposed to find the probability of winning exactly one match, no more than one match, or at least one match?

What are your thoughts? What have you tried? How far have you gotten? Where are you stuck?

Please be complete. Thank you!

If the probability of winning a single match is 0.1, what is the probability of losing a single match? Are we to assume that winning or losing a given match is "independent" of the other matches?

What is the probability of winning the first match but losing the other nine? What is the probability of winning the second match but losing the other nine? What is the probability of winning the third match but losing the other nine? Do you see the point? How many different such combinations are there?

HallsofIvy said:

If the probability of winning a single match is 0.1, what is the probability of losing a single match? Are we to assume that winning or losing a given match is "independent" of the other matches?

What is the probability of winning the first match but losing the other nine? What is the probability of winning the second match but losing the other nine? What is the probability of winning the third match but losing the other nine? Do you see the point? How many different such combinations are there?

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Right, I hadn't thought of all these things. Let's say the odds of winning just one, and then the odds of winning at least one.
Yea, assume that each match is independent. Yea I see your point, I just am not well developed enough with probabilities to think through it yet.

stapel said:

Are you supposed to find the probability of winning exactly one match, no more than one match, or at least one match?

What are your thoughts? What have you tried? How far have you gotten? Where are you stuck?

Please be complete. Thank you!

Click to expand...

I basically have not gotten anywhere, as I am having trouble wrapping myself around the logic. I just need help to understand the logic of probabilities. I understand that the odds of winning all ten is .1^10, but what would be the odds of winning just one, or more than one? If i have a 10% chance of winning one, certainly there is a much higher chance of winning one if I play ten, but it's obviously not 10%+10%...ten times over.

jamesldavis1 said:

I basically have not gotten anywhere, as I am having trouble wrapping myself around the logic. I just need help to understand the logic of probabilities. I understand that the odds of winning all ten is .1^10, but what would be the odds of winning just one, or more than one? If i have a 10% chance of winning one, certainly there is a much higher chance of winning one if I play ten, but it's obviously not 10%+10%...ten times over.

Click to expand...

That doesn't respond to Stapel's question which was "Are you supposed to find the probability of winning exactly one match, no more than one match, or at least one match?" Those are very different things. In my response, I assumed that you mean "exactly one match" but it would be nice to know for sure.

Can you, at least, answer the first question I asked. If the probability of winning one match is 0.1, what is the probability of losing one match?

jamesldavis1 said:

I basically have not gotten anywhere, as I am having trouble wrapping myself around the logic. I just need help to understand the logic of probabilities. I understand that the odds of winning all ten is .1^10, but what would be the odds of winning just one, or more than one? If i have a 10% chance of winning one, certainly there is a much higher chance of winning one if I play ten, but it's obviously not 10%+10%...ten times over.

Click to expand...

If you are going to a class for something like this, you need to review binomial distributions.

For this particular case, you have a 10% chance of winning so you have a 90% chance of losing. Suppose you play 100 times, playing two matches each time. Then (on average) you are going to lose 90 of the first matches. Of just those 90 matches, you are going to win 9 (10% of 90) of the second match. So the probabability of losing the first match and winning the second is 0.9 * 0.1. How about winning the first match and losing the second match? Well that's just 0.1 * 0.9 [win 10% of the first matches and lose 90% of those in which you won the first match]. So together, the chance of winning exactly one match is 2 * 0.1 * 0.9 = 18%

Is that enough to get you on your way?