Math
posted by Sam .
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
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
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
Respond to this Question
Similar Questions

Math/Probability
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 … 
Math
Consider a game where Ann and Bob play against each other in a dice game, Ann wins if her score is higher than Bob's, Bob wins if his score is higher or if the scores are the same. What is the probability of Ann winning? 
statistics
your teacher has invented a fair dice game to play. your teacher will roll one fair eight sided die and you will roll a fair six sided die. each player rolls once and the winner is the person with the higher number. in case of a tie … 
Physics
Bob and Bob Jr. stand at open doorways at opposite ends of an airplane hangar 25 m long. Anna owns a spaceship, 40 m long as it sits on the runway. Anna takes off in her spaceship, then swoops through the hangar at constant velocity. … 
physics
Bob and Bob Jr. stand at open doorways at opposite ends of an airplane hangar 25 m long. Anna owns a spaceship, 40 m long as it sits on the runway. Anna takes off in her spaceship, then swoops through the hangar at constant velocity. … 
linear algebra
Bob and Doug play a lot of PingPong, but Doug is a much better player, and wins 80% of their games. To make up for this, if Doug wins a game he will spot Bob five points in their next game. If Doug wins again he will spot Bob ten … 
Maths
X, Y and Z in that order throws a tetrahedral die the first throws a 4 wins. The game continues indefinitely until someone wins. Find the probability that X wins, Y wins and Z wins. 
Math
A game is played using one dice. If the dice is rolled and shows 1, the player wins $1; if it shows 2, the player wins $2; if it shows a 3, the player wins $3. If the die shows 4,5,or 6 the player wins nothing. a.) If there is a charge … 
Linear algebra
please help :( Bob and Doug play a lot of PingPong, but Doug is a much better player, and wins 90% of their games. To make up for this, if Doug wins a game he will spot Bob five points in their next game. If Doug wins again he will … 
algebra PLEASE help
Bob and Doug play a lot of PingPong, but Doug is a much better player, and wins 90% of their games. To make up for this, if Doug wins a game he will spot Bob five points in their next game. If Doug wins again he will spot Bob ten …