Difference between revisions of "2015 AMC 12B Problems/Problem 9"
Flamedragon (talk | contribs) (Created page with "==Problem== ==Solution== ==See Also== {{AMC12 box|year=2015|ab=B|num-a=10|num-b=8}} {{MAA Notice}}") |
Pi over two (talk | contribs) (→Problem) |
||
| Line 1: | Line 1: | ||
==Problem== | ==Problem== | ||
| + | Larry and Julius are playing a game, taking turns throwing a ball at a bottle sitting on a ledge. Larry throws first. The winner is the first person to knock the bottle off the ledge. At each turn the probability that a player knocks the bottle off the ledge is <math>\tfrac{1}{2}</math>, independently of what has happened before. What is the probability that Larry wins the game? | ||
| − | + | <math>\textbf{(A)}\; ? \qquad\textbf{(B)}\; ? \qquad\textbf{(C)}\; ? \qquad\textbf{(D)}\; ? \qquad\textbf{(E)}\; ?</math> | |
==Solution== | ==Solution== | ||
Revision as of 13:21, 3 March 2015
Problem
Larry and Julius are playing a game, taking turns throwing a ball at a bottle sitting on a ledge. Larry throws first. The winner is the first person to knock the bottle off the ledge. At each turn the probability that a player knocks the bottle off the ledge is 
, independently of what has happened before. What is the probability that Larry wins the game?
Solution
See Also
| 2015 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 8 |
Followed by Problem 10 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
