Tuesday, October 27, 2015
Unit 2 test, answer key.
Here is my answer key for the test review. I know Ms. Johnson sent hers out, but sometimes there are more than one way to get the same answer, so here is mine for comparison.
* Please note on page 5, if you had looked at my answer key already - I got one of them wrong. This image shows the correction, in blue ink!
Thursday, October 8, 2015
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)
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:
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)
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