Sample Problems

1) The World Series is a best-of-seven contest. (Two baseball teams play up to 7 games against each other. As soon as 1 team has won 4 games, the contest is over.) If teams A and B play in the series, a sequence of winners for the games played might be AAAA or ABBABAB, but could not be AAAAB.

How many different sequences of winners for the games of a World Series between Team A and Team B are possible?

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2) Two CUNY math professors arrange to meet to prepare a test. Each will arrive at a random time between 1:00 P.M. and 2:00 P.M. and will wait up to 15 minutes for the other before leaving.

What is the probability that the meeting takes place?

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3) Alice and Bob are bored and want to play a game. "I have an idea," Alice chimes in. "How about you flip this coin 2009 times and I'll flip it 2010 times and whoever gets more Heads wins?" Bob replies, "No, that's not fair! You're probably going to win since you get more flips!" "Fine!" answers Alice. "How about this? You flip the coin 2009 times and I'll flip it 2010 times and if I get more Heads, I win. If you get more Heads, you win. And, if there's a tie, we'll say that you win too." Bob shrugs his shoulders and agrees to play. What's the probability that Alice wins the game? Prove your answer.

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