Probability Unit, continued... Pascal's triangle, theoretical probability, expected value.

Here are some things to help you with the homework assignments, or your project:

We did a problem about a guy who had 5 chances to hit a pitched baseball. We did it with both a tree:

and with Pascal's triangle:

Pascal's triangle is useful whenever you have a BINOMIAL game (hit/miss, even/odd, yes/no, heads/tails) where both probabilities are equally likely.

NOTE: If your game is NOT binomial, there are other methods to use. We will get to them Thursday/Friday (today and tomorrow) in class.

No matter what kind of game you have, your report should include a budget section like this:

There was a homework assignment about a girl shooting baskets for different $ allowance values. Here are the pictures from that:

On the first shot, she will make the basket 60% of the time, and miss 40% of the time. So 40 of the 100 boxes in the area model are marked off, and the reward for that is just $5.

If she makes the first shot (60 of the original 100 boxes), she will make the next shot 60% of the time.

60% = 0.60.  0.60(60) = 36, so in 36 of the original 100 boxes, she gets the full $25. That's 36%.

40% of the time she misses that 2nd shot. 40% = 0.40.  0.40(60) = 24, so in 24 of the original boxes she gets the $15 reward (according to the rules of the game). That's 24%

Note, 40% + 36% + 24% = 100%.

She does that every week for a year (52 weeks):

In theory, she will earn just $5 in 40% of those 52 weeks:  0.40(52)*$5 = $104.00
In theory, she will earn $15 in  24% of those 52 weeks:      0.24(52)*$15 = $187.20
In theory, she will earn the full $25 in 36% of those 52 weeks: 0.36(52)*$25 = $430.56

So, adding up all those means she can EXPECT to earn, over the year, a total VALUE of $759.20.

(The EXPECTED VALUE is $759.20)