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#26 Re: Help Me ! » Proof by Induction Problem » 2007-09-15 10:08:59
Wow, quick response. Its interesting to see Daniel's method too. Thanks a lot guys! 
#27 Help Me ! » Proof by Induction Problem » 2007-09-15 07:50:25
- MarkusD
- Replies: 5
Hey everyone,
Ive been trying to get my head around induction but I am having a hard time working around it. Im stuck on the following problem:
Prove that the sum of the first n odd integers is equal to n^2.
Anyone have any insight as to how to set this up using mathetmatical induction?
#28 Re: Help Me ! » Conditional Probability and Lottery Question » 2006-10-08 09:06:20
Not exactly.
"What is the probability of getting the 5th number right provided that the first 4 were correct?" means that the first 4 are already correct and so you don't need to work out probabilities for them, you just need to work out the chance that the 5th will be correct as well.
hmmm, what if the word "provided" was changed to "condtioned on"? Would that make a difference?
I guess my confusion is that we know before making
the last draw that the first four draws were correct, which is contrasted from the other example of getting all 5 numbers correct because this probability is calculated before the result of the drawing is known.
In my head Im thinking P(5th draw being correct|1st, 2nd, 3rd, and 4th number was correct) and I dont know what the bayesian formula would be. Or why I wouldnt need it.
#29 Re: Help Me ! » Conditional Probability and Lottery Question » 2006-10-08 07:20:32
Thanks for the reply!
I see that youre using combinations or at least I got the same answers as you did using
n!/r!(n-r)!
for the first case, and:
n!/(n-r)!
for the second.
I was trying to use conditonal probability earlier like P(B|A) = P(A&B)/P(A). I was trying to answer the question: what is the probability of getting the 5th number right provided that the first 4 were correct? Is that equivalent to the question "what is the probability of getting all 5 numbers correctly (assuming order doesnt matter, and what is the answer if order does matter)?"
#30 Help Me ! » Conditional Probability and Lottery Question » 2006-10-08 05:38:29
- MarkusD
- Replies: 4
Hey everyone, first post here and I have a few questions about a lottery:
If you have a lottery and you have to pick 5 numbers between 1-37 (with each number only able to be drawn once) whats the probability of getting all 5 numbers the same? Whats the probability of getting all 5 numbers in the same order as the drawing. And why are the odds of winning in the former case 1 in 435,897?
I tried using conditional probability but Im not sure how to use beyond two events.