Two gamblers A and B play a game throwing two ordinary dice. A wins if he obtains the sum 6 before B obtains 7, and B wins if he obtains the sum 7 before A obtains 6. Which of the players has a better chance of winning if player A starts the game?
Show your full solution so that it can be understood easily.
Probability :Two gamblers
- Fahim Shahriar
- Posts:138
- Joined:Sun Dec 18, 2011 12:53 pm
Name: Fahim Shahriar Shakkhor
Notre Dame College
Notre Dame College
- Fahim Shahriar
- Posts:138
- Joined:Sun Dec 18, 2011 12:53 pm
Re: Probability :Two gamblers
A few months ago I couldn't solve that one. But now I can.
Learning...
Prob of $A = \dfrac {5}{36} = \dfrac {180}{36^2}$
Prob of $B = \dfrac {6}{36} \times \dfrac {31}{36} = \dfrac {186}{36^2}$
So $B$ has better chance.
Learning...
Prob of $A = \dfrac {5}{36} = \dfrac {180}{36^2}$
Prob of $B = \dfrac {6}{36} \times \dfrac {31}{36} = \dfrac {186}{36^2}$
So $B$ has better chance.
Last edited by Phlembac Adib Hasan on Thu Feb 21, 2013 7:42 pm, edited 2 times in total.
Reason: In inline math, use \dfrac instead of \frac command.
Reason: In inline math, use \dfrac instead of \frac command.
Name: Fahim Shahriar Shakkhor
Notre Dame College
Notre Dame College
Re: Probability :Two gamblers
Does 'Prob of $A$' in your calculation mean the probability of A's winning or the probability of just getting the sum 6 in any throw of the dices? Your conclusion is right, but not the reasoning you provided in your comment, especially because the dice throwing may go on for round after round before one is finally the winner, but you have considered only two rounds of throwing in total.
- Fahim Shahriar
- Posts:138
- Joined:Sun Dec 18, 2011 12:53 pm
Re: Probability :Two gamblers
You're right. I thought it to be a two round game. Even I missed the first round. Then I have to calculate the probability for every possible rounds. It's full of calculations but not difficult. Isn't there any one liner solution ? I saw someone giving the solution in just one line in fb but can't remember.
Name: Fahim Shahriar Shakkhor
Notre Dame College
Notre Dame College