SOLUTION: Amy and Martin play a game in which they take turns flipping a fair coin until one of them flips a head. The first person to flip a head is the winner. If Amy goes first, find the

Algebra ->  Probability-and-statistics -> SOLUTION: Amy and Martin play a game in which they take turns flipping a fair coin until one of them flips a head. The first person to flip a head is the winner. If Amy goes first, find the       Log On


   



Question 248695: Amy and Martin play a game in which they take turns flipping a fair coin until one of them flips a head. The first person to flip a head is the winner. If Amy goes first, find the probability that she wins.
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Chances of winning on that flip before the game begins.
A==M
1/2 1/4
1/8 1/16
1/32 1/64
.
1/8 / 1/2 = 1/4
1/32 / 1/8 = 1/4
This is an infinite geometric sequence.
r=1/4=.25
S=a%5B1%5D%2F%281-r%29=.5%2F%281-.25%29=.5%2F.75=2%2F3 Amy's probability of winning.
.
Ed