MathDB

18

Part of 2005 AMC 10

Problems(2)

Two Teams in a Series

Source:

1/12/2009
Team A A and team B B play a series. The first team to win three games wins the series. Each team is equally likely to win each game, there are no ties, and the outcomes of the individual games are independent. If team B B wins the second game and team A A wins the series, what is the probability that team B B wins the first game? <spanclass=′latex−bold′>(A)</span> 15<spanclass=′latex−bold′>(B)</span> 14<spanclass=′latex−bold′>(C)</span> 13<spanclass=′latex−bold′>(D)</span> 12<spanclass=′latex−bold′>(E)</span> 23 <span class='latex-bold'>(A)</span>\ \frac{1}{5}\qquad <span class='latex-bold'>(B)</span>\ \frac{1}{4}\qquad <span class='latex-bold'>(C)</span>\ \frac{1}{3}\qquad <span class='latex-bold'>(D)</span>\ \frac{1}{2}\qquad <span class='latex-bold'>(E)</span>\ \frac{2}{3}
probability
Counting David's Telephone Numbers

Source:

1/14/2009
All of David's telephone numbers have the form 555\minus{}abc\minus{}defg, where a a, b b, c c, d d, e e, f f, and g g are distinct digits and in increasing order, and none is either 0 0 or 1 1. How many different telephone numbers can David have? <spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 7<spanclass=′latex−bold′>(D)</span> 8<spanclass=′latex−bold′>(E)</span> 9 <span class='latex-bold'>(A)</span>\ 1\qquad <span class='latex-bold'>(B)</span>\ 2\qquad <span class='latex-bold'>(C)</span>\ 7\qquad <span class='latex-bold'>(D)</span>\ 8\qquad <span class='latex-bold'>(E)</span>\ 9