Posted by Sam on Monday, May 31, 2010 at 10:38pm.
Anna and bob play a game in which Anna begins by rolling a fair dice, after which bob tosses a fair coin. They take turns until one of them wins. Anna wins when she rolls a 6. Bob wins when the coin lands on heads. What is the probability that Anna will win the game?
Well there are a number of ways for Anna to win like 1st it is 1/6 the second way can be 5/6*1/2*5/6*1/2*1/6 etc. Where do i go from here to find an exact number for the probability?

Math  PsyDAG, Tuesday, June 1, 2010 at 11:20am
What happens if Anna rolls the 6 and Bob tosses a head? It it considered a tie, or does one or the other automatically win? This will change the probability of Anna winning the game.

Math  moe, Saturday, September 11, 2010 at 4:45pm
So, if Ana rolls a 6, does the game end instantly, or does Bob get to flip a coin one last time? If he does, and gets a head, does the game continue or do they declare it a tie?
Does the question really ask for the probability that Ana wins the game, or does it ask for the probability that she wins the game within a certain number of rounds?
On Ana's first roll, she has a 1/6 chance of getting a 6.
In order to get to a second roll, she needs to roll something other than a 6 on her first roll, and Bob needs to get a tails. The probability of that happening is 5/6 * 1/2 = 5/12. Then she has a 1/6 chance of getting a 6 on her 2nd roll, so the probability that Ana wins on her second roll is 5/12*1/6 = 5/72.
probability that she wins on her third roll is 5/6*1/2*5/6*1/2*1/6=25/864
So far, the probability that she wins in three rolls or less is 1/6 + 5/72 + 25/864
This looks like a geometric series, with r=5/12.
Sum of an infinite geometric series is a1/(1r) where a1= the first term = 1/6
a1/(1r)=(1/6) / (7/12) = 2/7
Answer This Question
Related Questions
 Math/Probability  Anna and bob play a game in which Anna begins by rolling a ...
 Physics  Bob and Bob Jr. stand at open doorways at opposite ends of an airplane...
 physics  Bob and Bob Jr. stand at open doorways at opposite ends of an airplane...
 linear algebra  Bob and Doug play a lot of PingPong, but Doug is a much better...
 Math  Consider a game where Ann and Bob play against each other in a dice game...
 statistics  your teacher has invented a fair dice game to play. your teacher ...
 Math  A game is played using one dice. If the dice is rolled and shows 1, the ...
 Maths  X, Y and Z in that order throws a tetrahedral die the first throws a 4 ...
 math  A game is defined by the rules that two dice are rolled and the player ...
 Quantitative method probability  X, Y and Z in that order throws a tetrahedral ...
More Related Questions