Enigma 1414: World series
From New Scientist #2574, 21st October 2006
Baseball’s so-called World Series is won by the first of the two teams involved to win four matches. Since matches cannot be tied, that means that it may be decided in 4, 5, 6 or 7 matches. Matches 1 and 2 are held on Team A’s ground, matches 3, 4 and (if required) 5 on Team B’s ground, and (if required) matches 6 and 7 on Team A’s ground.
1. Assume that each team has an equal chance of winning each match and tell me what, as a percentage expressed to as many decimal place as are necessary, is the probability that (a) the same number of matches will be played on each ground; (b) match 7 will be played.
2. Now assume that there is a 60 percent probability that any match will be won by the home team and answer questions (a) and (b) above.