SOLUTION: Goliath and David play a game in which there are no ties. Each player is equally likely to win each game. The first player to win 4 games becomes the champions and no further game

Question 1108717: Goliath and David play a game in which there are no ties. Each player is equally likely to win each game. The first player to win 4 games becomes the champions and no further games are played. Goliath wins the first 2 games. What is the probability that David becomes the champion ?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
since Goliath has won the first two games, David could win the next 4 games or loose one more game - 6 or 7 games to be played
:
the probability for each player to win a game is 1/2
:
let L be a loss for David and W be a win for David
:
we have the following
:
(L,L,W,W,W,W), (L,L,L,W,W,W,W), (L,L,W,L,W,W,W), (L,L,W,W,L,W,W), (L,L,W,W,W,L,W)
:
(1/2)^6 + 4 * (1/2)^7 = 0.0469
:
P ( David is the Champion ) = 0.0469
:
RELATED QUESTIONS
goliath and David play a game in which there are no ties. Each player is likely to win... (answered by Theo)

In a basketball tournament, there are four teams, and each team plays against every other (answered by CPhill,ikleyn)

sam.matt,and travis are playing a game, they each toss 1 quarter and 1 dime. in order to... (answered by stanbon)

In a game, the player and the house each roll a die. Whoever gets the higher number... (answered by its.evapatel)

There are two stacks of cards that each contain "r" cards. Two players play the following (answered by Edwin McCravy,solver91311)

in a chess competition , some boys and some girls are involved, every students have to... (answered by Danielshinmath)

Candace and Darryl are playing a game with piles of beans. On each player�s turn, they... (answered by ikleyn)

Two friends A and B play a checkers match which will end when one player has won three... (answered by robertb,ikleyn)

at a carnival samantha plays a dart game that has a $100 gift certificate prize. To win... (answered by AxasSuoh)