Probability help

[JellyFish]

I tried doing this question using a tree diagram like in a text book but it seemed to confuse me more. If anyone could even give me the first step or point me in the right direction I would be very grateful.

The Blue Jays are leading the Yankees one game to none in a best-of-five playoff series. After a win, the probability of Blue Jays winning is 60%, while after a loss their probability of winning drops by 5%. The first team to win three games take the series. Assume that there are no ties. What is the probability of the Yankees coming back to win the series?

 

[DrMike]

A tree will work - each node will have two branched going to the next level - one for a Blue Jays win, the other for a Yankees win. The maximum depth of the tree will be 4, since one game of the 5 is already played. To work out the probabilities, follow carefully the rules they gave.

Otherwise, you might like to make a list of all possible outcomes for the next few games - there are at most 16 possibilities (actually less).

Eg, your list might start :

BB
BYB
BYYB
BYYY
etc

Work out the probabilities of each (use the rules they gave to find the probabilites)... eg

P(BYB) = P(B wins after a win) x P(B loses after a win) x P(B wins after 1 loss) = 0.6 x 0.4 x 0.55 = 0.132

then add up the probabilities of those combinations that mean "Yankees win the series",

P(Yankees win the series) = P(BYYY) + P(YBYY) + ...

Hope that helps!

 

[JellyFish]

Thanks.

I ended up using a tree and finding that there were 10 different ways to end the series, 4 of which the Yankees won the series.

I carried the 4 probabilities of the Yankees winning the series then added them together to get a probability of 0.2385.

Thanks again