Posted by Sam on Monday, May 31, 2010 at 10:38pm.
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.
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/(1-r) where a1= the first term = 1/6
a1/(1-r)=(1/6) / (7/12) = 2/7
Related Questions
Math/Probability - Anna and bob play a game in which Anna begins by rolling a ...
Math - The game of dots is played by rolling a fair dice and receiving $1 for ...
math - In rolling a pair of dice, suppose you win $5 if the sum is 10 but lose $...
math stuff - suppose to arrage the names of the ppl in descending order of their...
Math-Fair Game question - the game of dots is played by rolling a fair die and ...
Stats HELP PLEASE - The game of Yahtzee is played with five fair six-sided dice...
math fair - The game of dots is played by rolling a fair die and receiving $1 ...
Math - Consider a game where Ann and Bob play against each other in a dice game...
Math - Suppose you play a game in which two fair standard dice are rolled. If ...
English - Playing the dice game, have a conversation about what you must do and ...
For Further Reading
