Question

Suppose that the new england colonials baseball team is equally likely to win a game as not to win it. if 4 colonials games are chosen at random, what is the probability that exactly 2 of those games are won by the colonials

Answer 1

1. Consider the tree diagram in the picture attached.

2 Each of the games picked can be a W (win) or a L (lose), the chances are equal

3. All that could happen in 4 picked games is shown in the picture:

2 w 2 l can happen in the following 6 ways: {(W,W,L,L)(W,L,W,L)(W,L,L,W)(L,W,W,L)(L,W,L,W)(L,L,W,W)}

4. P(2W,2L)=6/16=3/8