probability question

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jimmyjay

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Hi, If a lawyer has a 50% probability of winning each of his lawsuits,
what is the probability of a lawyer winning 20 consecutive lawsuits?
I am unsure if I need to add the probability or multiply the probability?
Can anyone shed light on this for me?
Thanks.
 
Consider some positive number less than 1. Can you add up that number enough times to get a sum over 1? If that positive number is a/b then if you multiply it by b/a you will get 1. Now there is an integer (actually infinitely many) that is greater than b/a. Call one such integer Q. Then (a/b)*Q>1. Now remember that multiplication is just repeated addition, ie (a/b)Q = (a/b) + (a/b) + ... + (a/b) >1
Now think about what this would mean if the 20 in your problem is replaced with Q or any number greater than Q. Do you see what I am getting out?
 
jimmyjay said:
Hi, If a lawyer has a 50% probability of winning each of his lawsuits,
what is the probability of a lawyer winning 20 consecutive lawsuits?
I am unsure if I need to add the probability or multiply the probability?
Can anyone shed light on this for me?
Thanks.
Click to expand...
Since the lawyer has a 50% chance of winning a lawsuit this is like tossing a coin. If the coin lands on head the lawyer wins, if the coin lands on tails the lawyer loses. See what happens with 3 cases. So list the sample space with either w or l OR h or t.
The sample space is hhh, thh, hth, hht, htt, tht, tth, ttt, There are 8 possible outcomes and only one has hhh. So the probability of the lawyer winning 3 cases in a row is 1/8. Now you need to think if 1/8 came from addition or multiplication.
If you do not see a solution with large numbers, like 20, then try it with smaller number!
 
Thanks for your reply, I understand the first reply i.e. if there are 8 possible outcomes (1/8) then it must be multiplication as addition would only give a 1/6 probability..so the probability of a lawyer winning 20 consecutive lawsuits would be 1 in 1,048,576?
 
jimmyjay said:
Thanks for your reply, I understand the first reply i.e. if there are 8 possible outcomes (1/8) then it must be multiplication as addition would only give a 1/6 probability..so the probability of a lawyer winning 20 consecutive lawsuits would be 1 in 1,048,576?
Click to expand...
Sorry but you are not understanding as 1/2 + 1/2 + 1/2 is NOT 1/6. 1/2 >1/6!!! So how can you add 1/2 to itself three times and get 1/6. It seems that you missed my whole point above. 1/2 + 1/2 + 1/2 = 1 1/2 which is greater than 1. You can always add a positive number that is less than 1 enough times to get over 1. For example if you add 1/20 to itself more than 20 times you will get more than 1. 1st learn how to add fractions and learn how to tell that some results you get must be wrong. Then re-read my comment above.
 
Thanks, I read how to add fractions, which makes it easier to understand and can see that adding the fractions wouldn't work in this scenario.
I need to multiply the fractions which gives a 1 in 1,1048, 576 probability of a lawyer winning 20 consecutive lawsuits (assuming a 50%;50% probability in each case). Just seems to be a very unlikely probability!
 
I think that you meant to write 1 in 1,048, 576
Do you think that 1/1,048,576 is about right for tossing heads 20 times in a row?
 
Yes, I mean 1 in 1,048, 576 :)
I would have thought it was much more likely than odds of 1/1,048,576 ..
 
I feel that this lawyer did not study very hard in law school.
 
jimmyjay said:
Hi, If a lawyer has a 50% probability of winning each of his lawsuits,
what is the probability of a lawyer winning 20 consecutive lawsuits?I am unsure if I need to add the probability or multiply the probability?
Click to expand...
If that lawyer flipped a single coin repeatedly the probability of 20 consecutive heads is \(\displaystyle \dfrac{1}{2^{20}}\).
 
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