# rolling two dices probability problem

• Aug 28th 2007, 10:26 PM
rbenito
rolling two dices probability problem
anybody can help with the next problem:?
A game begins by choosing between dice A and B is some manner such that the probability that A is selected is 'p'. The die thus selected is then tossed until a white face appears, at which time the game is conluded. Die a has 4 red and 2 white faces. Die B has 2 red and 4 white faces. After playing this game a great many times, it is observed that the probability that a game is concluded in exactly three tosses of the selected die is 7/81. Determine the value of p.

cheers...
• Aug 28th 2007, 11:01 PM
CaptainBlack
Quote:

Originally Posted by rbenito
anybody can help with the next problem:?
A game begins by choosing between dice A and B is some manner such that the probability that A is selected is 'p'. The die thus selected is then tossed until a white face appears, at which time the game is conluded. Die a has 4 red and 2 white faces. Die B has 2 red and 4 white faces. After playing this game a great many times, it is observed that the probability that a game is concluded in exactly three tosses of the selected die is 7/81. Determine the value of p.

cheers...

Suppose die A is selected, then the probability that the game ends in exactly three tosses is (4/6)(4/6)(2/6)

Suppose die B is selected, then the probability that the game ends in exactly three tosses is (2/6)(2/6)(4/6)

Thus if die A is selected with probability p the probability that the game ends in exactly 3 moves is:

p [ (4/6)(4/6)(2/6) ] + (1-p) [ (2/6)(2/6)(4/6) ] = 7/81

Now solve for p.

RonL
• Aug 29th 2007, 06:15 PM
rbenito
Thank you very much
The solution seems very simple, thank you.