# Probability of dice rolls

• May 6th 2013, 04:26 PM
verasi
Probability of dice rolls
I can't get get the correct answer for a question. The question is: Bob and Roy play a game in which they roll 2 unbiased 6-faced dice. The first one who rolls a sum of 6 wins.
a) What is the probability that Kassanthra wins on her second roll?
b) What is the probability that George wins on his second roll?

a) (5/6)(1/6)=0.139
b) (1-0.139)(5/6)(1/6)=0.120

a) 0.103
b) 0.0887

What am I doing wrong?
• May 6th 2013, 07:29 PM
chiro
Re: Probability of dice rolls
Hey verasi.

If you have two dice, then the probability of getting a sum of 6 is given by the combinations (1,5), (5,1), (2,4), (4,2) and (3,3). They all have a probability of 1/36 which means P(Sum = 6) = 5/36 and the P(Sum != 6) = 31/36

The question I have to ask before I continue, is a "second" roll another pair of rolls or is it the second part of the pair for the first pair of rolls?
• May 6th 2013, 07:53 PM
majamin
Re: Probability of dice rolls
Confusing for the fact that you mention Bob and Roy, but ask about Kassanthra and George. In any case, the probability for someone to win on their second roll: that person would have to lose their first roll, their opponent to lose their first roll, and then the person wins the second roll (product of three probabilities). By the way, the probability that you win is not 1/6. Count the number of ways to roll a 5 again.
• May 7th 2013, 11:51 AM
verasi
Re: Probability of dice rolls
Quote:

Originally Posted by majamin
Confusing for the fact that you mention Bob and Roy, but ask about Kassanthra and George. In any case, the probability for someone to win on their second roll: that person would have to lose their first roll, their opponent to lose their first roll, and then the person wins the second roll (product of three probabilities). By the way, the probability that you win is not 1/6. Count the number of ways to roll a 5 again.

Oh yah thanks I misread the question. But the probability is 1/6 (number of dice u can roll to get a 6 after u roll the first dice). But the step is a bit repetitive cause I kinda misunderstood the question.
• May 7th 2013, 01:34 PM
ebaines
Re: Probability of dice rolls
chiro had it right: the probability of rolling a 6 (not 5) on any roll is 5/36. Which means the probability of rolling something other than a 6 is 1-5/36 = 31/36.

If the players take alternating turns with Bob going first then he wins on the second roll if first he rolls something other than 5, then Ray rolls something other than 5, then Bob rolls a 5. That probability of that sequence occurring is (31/36) x (31/36) x (5/36) = 0.1030.

For Ray to win on his second turn the probability is (31/36) x (31/36) x (31/36) x 5/36) = 0.0887.
• May 7th 2013, 04:47 PM
verasi
Re: Probability of dice rolls
Yah thanks I got it now