My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
October 30th, 2013, 01:23 PM   #1
Senior Member
 
Joined: Oct 2009

Posts: 895
Thanks: 1

Two players A and B play a game of dice .

Two players A and B play a game of dice . They roll a pair of dice alternately . The player who rolls 7 first wins . If A starts then find the probability of B winning the game ?

please help me how I can solve this question
r-soy is offline  
 
October 30th, 2013, 01:47 PM   #2
Senior Member
 
Joined: Feb 2012

Posts: 628
Thanks: 1

Re: Two players A and B play a game of dice .

Well, the probability of rolling a 7 is 1/6, so the probability of not rolling a 7 is 5/6.

If A goes first, he must not roll a 7 in order for B to win. So this has a 5/6 chance of occurrence. Then, if B rolls a 7, B wins. This has a chance of 1/6. So the probability of B winning after one round is . But this is the probability of B winning in any round, given that neither player has won yet.

The probability that neither player wins in a given round is .

Hence, the probability that B wins in the nth round is .

The probability that B wins is then .
icemanfan is offline  
October 30th, 2013, 01:59 PM   #3
Senior Member
 
Joined: Oct 2009

Posts: 895
Thanks: 1

Re: Two players A and B play a game of dice .

How you got
A ) that the probability of rolling a 7 is 1/6 ?

B ) the probability that neither player wins in a given round is 25/36

thanks
r-soy is offline  
October 31st, 2013, 11:37 AM   #4
Senior Member
 
Joined: Feb 2012

Posts: 628
Thanks: 1

Re: Two players A and B play a game of dice .

A) There are 36 possible rolls for two dice, since there are 6 possibilities for the first die and 6 possibilities for the second die. Of these, there are 6 combinations that yield a sum of 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1). This gives a chance of rolling a 7.

B) Since there is a 1/6 chance of either player rolling a 7, there is a 5/6 chance that A will not roll a 7, and a 5/6 chance that B will not roll a 7. Since these two events are independent, the probability of both of them occurring in one round is the product of both chances, which is .
icemanfan is offline  
October 31st, 2013, 12:44 PM   #5
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 8,788
Thanks: 607

Re: Two players A and B play a game of dice .

Quote:
Originally Posted by r-soy
How you got
A ) that the probability of rolling a 7 is 1/6 ?
Example:
1st roll : 3
2nd roll: only a 4 will make 7, so 1/6

Works similarly for any 1st roll result: 1-6, 2-5, 3-4, 4-3, 5-2, 6-1
Denis is offline  
October 31st, 2013, 03:49 PM   #6
Senior Member
 
Joined: Oct 2009

Posts: 895
Thanks: 1

Re: Two players A and B play a game of dice .

thanks all now is clear
r-soy is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
dice, game, play, players



Search tags for this page
A and B throw alternatively with a pair pf dice A wins if he throws
,

a and b throw alternatively with a pair of dice

,

A and B play by throwing a pair of dice alternately. A wins if he throws 6 before B throws 7. If A starts the game their chances of wining the game are

,

A and B play dice alternately the one who gets 6 first wins probability

,

A and B thrown a die.the one who throws 2 first win.if A starts to thrown find their chances of winning.

,

two players,AandB,through a pair of dice.A, who starts the game, wins if he throws six before B throws 7,and B wins if he throws 7 before A throws six.Obtain the probability that A will win the game

,

what is the probability of winning A if he gets 6 when he 1st throw a dice

,

a game consists of two players a and b rolling a die alternatively. the one who gets 5 on die first wins the game. if a starts the game what are the winning chances of a and b

,

two players roll a dice alternately

,

A throw 7 and B wins if A throw 7

,

a and b alternatively throws a pair of dice a wins if he throws 7 and b wins if he throws 7 before a

,

a and b throw alternatively a pair of dice

,

Twoplayers A andB toss a dicealternately he who first through a 'five' winsthe game. If A begins whatis the probability thathe wins

,

a b throw a dice alternately. the one who gets 5. firstwins a starts

,

two persons a and b throws alternately with a pair of dice .a win if he throws 6 before b throws 7 and b wins if he throws 7 before a throws 6 .if a begins find the probability of winning?

Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Turing complete game 2 AIs can play to measure intelligence BenFRayfield Math Events 0 February 20th, 2014 12:39 PM
Dice Game PrayForStan Algebra 3 November 30th, 2012 07:10 AM
The Hardest Math Game You'll Ever Play DamballahWeddo New Users 3 August 4th, 2010 03:31 PM
I want to play a game.. rv74 Algebra 0 October 30th, 2008 05:16 AM
Dice Game PrayForStan Number Theory 0 January 1st, 1970 12:00 AM





Copyright © 2017 My Math Forum. All rights reserved.