Problem of the Week 10

One of two cubical dice has a blank face rather than one dot.  The other die has a blank face rather than four dots.  What is the probability that a sum of seven appears when the dice are thrown?

 

Alternate Problem 10

Three people each toss a penny at the same time.  What is the probability that two people get the same side of the penny and the other person gets the opposite side?

 

Extension Problem 10

To win a play-off championship, a team must win the best out of five games.  Whichever team wins three games first wins the series.  In how many different ways can a team win the play-off?

For the baseball World Series, a team must win four out of seven.  In how many ways can a team win the World Series?