All homework is to be done on graph paper to be handed in. Problem of the week is due on Tuesday. Spelling and neatness count, all work must be shown for credit.
Problems A local youth baseball league has a league championship series that determines which team is that year’s champion. The youth league championship series is set up like the MLB World Series – it’s a best of seven series. Suppose the Cardinals and the Orioles are the two teams in the championship series and each has a probability of 1/2 of winning any given game in the championship series.
What is the probability that the Cardinals will win the series in exactly 4 games? Remember the chance of winning each game is 1/2. Use the Probability of compound events rule - multiply the probability of the first event by the probability of the second event etc. If the probability of each event was 1 the answer would be 4/7 but it is not one.
What is the probability that the Orioles will win the series in exactly 6 games?
For this to happen the Orioles would have to win 4 and the Cardinals win 2.
THis is a tough one. THIS would be ten combinations of 1/2 odds - how would you find this?
What is the probability that the series will last all 7 games? For the series to go to the 7th game, each team would have to win 3 of the six previous games. THis means that we can determine the munber of ways each team can win 3 out of 6 games by solving 6 choose 3 - number of permutations over total number of permutations. THere are 20 possible ways and we know the probability of each way
Grade 6 did not learn factorials yet.