Suppose your school's basketball team is playing a four-game

[lisa.]

Hey,

Suppose your school's basketball team is playing a four-game series against another school. So far this season, each team has won three of the six games in which theuy faced each other.


a) draw a tree diagram to illustrate all possible outcomes of the series.
b) Use your tree diagram to determine the probability of your school winning exactly two games.
c)What is the probability of your school sweeping the series(winning all four games?

This is what I've done so far...

a)

is this the right way to draw the diagram ? and the answer is 3/8 I couldn't figure out why it is 3.

Thanks

 

[soroban]

Re: Suppose your school's basketball team is playing a four-

Hello, Lisa!

Suppose your school's basketball team is playing a four-game series against another school.

This next statement is puzzling.
So far this season, each team has won three of the six games in which they faced each other.
Who cares what happened in the past?

a) Draw a tree diagram to illustrate all possible outcomes of the series.

b) Use your tree diagram to determine the prob. of your school winning exactly 2 games.

c) What is the probability of your school sweeping the series (winning all four games)?

(a)                                   o
                                  *       *
                              *               *
                          *                       *
Game 1                A                               B
                    /   \                           /   \
                  /       \                       /       \
                /           \                   /           \
Game 2        A               B               A               B
            /   \           /   \           /   \           /   \
Game 3    A       B       A       B       A       B       A       B
         / \     / \     / \     / \     / \     / \     / \     / \
Game 4  A   B   A   B   A   B   A   B   A   B   A   B   A   B   A   B

        1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16

Assume that "our" team is \(\displaystyle A\).

(b) \(\displaystyle A\) wins exactly two games in outcomes: #4, 6, 7, 10, 11, 13.
Therefore: \(\displaystyle P(\text{win two games}) \:=\:\frac{6}{16}\:=\:\L\frac{3}{8}\)

(c) \(\displaystyle A\) sweeps the series in outcome #1 only.
Therefore: \(\displaystyle P(\text{sweeps series}) \:=\:\L\frac{1}{16}\)

 

[lisa.]

Thanks for your help Soroban

Lisa