It has been a long time between now and my last math class - so nomenclature is likely off.
I have a question about combining probabilities. I will ask generally for help how to solve the probability question - and then give you the specifics of the problem I would like to have solved.
Definition = P[A] = probability of event A happening.
So let's say I know the probability of event A happening before event B, and the probability of event C happening before event B.
What is the probability of event A and C happening before B?
What about the probability of event C happening twice, or event A happening once, before event B happens twice?
Now for more specifics. I am looking at two 6 sided dice.
P[A] = Rolling a 7 = .1666
P = Rolling a 10 = .13333
P[C] = Rolling a 4,5,6,8 or 9 = .58333
What is the probability of P[A] once OR P[C] seven times before P happening twice, OR P[A] once or P[C] fourteen times before the P happens three times, OR rolling P[A] once or P[C] 28 times before P happens 4 times?
What I know.
The probability of P happening five times before P[A] is (1/3)^5 =.004115. One can expect this 4 times in a game of 1000 throws (right?).
The probability of P[C] happening 7 times before P is (0.875)^7 = .393. One can expect this to happen 39.3% % of the time.
I just don't now how to combine those known numbers to come up with the answer.
Thanks for any help.
I have a question about combining probabilities. I will ask generally for help how to solve the probability question - and then give you the specifics of the problem I would like to have solved.
Definition = P[A] = probability of event A happening.
So let's say I know the probability of event A happening before event B, and the probability of event C happening before event B.
What is the probability of event A and C happening before B?
What about the probability of event C happening twice, or event A happening once, before event B happens twice?
Now for more specifics. I am looking at two 6 sided dice.
P[A] = Rolling a 7 = .1666
P = Rolling a 10 = .13333
P[C] = Rolling a 4,5,6,8 or 9 = .58333
What is the probability of P[A] once OR P[C] seven times before P happening twice, OR P[A] once or P[C] fourteen times before the P happens three times, OR rolling P[A] once or P[C] 28 times before P happens 4 times?
What I know.
The probability of P happening five times before P[A] is (1/3)^5 =.004115. One can expect this 4 times in a game of 1000 throws (right?).
The probability of P[C] happening 7 times before P is (0.875)^7 = .393. One can expect this to happen 39.3% % of the time.
I just don't now how to combine those known numbers to come up with the answer.
Thanks for any help.