Alas, here's your chance to finally learn to like probability. We'll be covering the important stuff and giving you the opportunity to extend your understanding through an optional challenge. The test will be on Thursday, November 17. On Friday, November 18th we will have our annual casino day. We would appreciate adult help on this day, especially from parents who have some experience watching chips pass back to the "house." If you want to design a casino game of chance where you will be the "house" and the students will play against you, see Mrs. L this week.
Please be safe on Tuesday. Good luck to the GHP interviewees. See you all on Wednesday.
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RE: problem 6.32 from the textbook
Warning: I am not advocating gambling in any way, shape or form. In fact, I am trying to help you understand the mathematics of this game so you DON'T lose your money.
OK, it has been suggested that a person could win at roulette if he bet on 34 of the 38 available numbers.
The rationale is that you would almost always win and you would get 36 chips for the 34 that you bet. Ah, you'd be up by two chips!
Here's a way to simulate 100 spins of the wheel. Assume that you are selecting the numbers 1 through 34 and that 35, 36, 0 and 00 are the numbers you didn't cover. By running RandInt(1,38,100) on your calculator you simulate the spinning of the next 100 winning numbers. We assume that 37 and 38 represent 0 and 00. If the number selected is in [1,34], then you have paid out 34 chips, but you get 36 back, for a net gain of 2. If the number is [35,38], then you lost all of your 34 chips. The likelihoods for these events are 34/38 and 4/38, respectively.
Therefore, the expected value equation for this perspective is (34/38)*2 + (4/38)*(-34), where breaking even would be an expected value of 0.If you wanted to use the perspective of how much of your 34 chip wealth you would have after the roll, (34/38) of the time you would have 36 chips, while 4/38 of the time you would have nothing. Breaking even would mean that the expected value was equal to 34 chips (your wealth before the spin).
Don't believe me yet? Go ahead and generate those 100 random values and store them in L1. Then compute the net payoff for each one [L1<35)*36-34] in L2. Find the sum of L2. Negatives indicate that you lost money. Maybe even a lot of money.
If you store the formula for the net payoff in L2 as a locked formula, you can do this calculation in one step from the home screen:
RandInt(1,38,100)[STORE]L1:Sum(L2)
If you haven't stored the formula, I suppose you could calculate it from the home screen:
RandInt(1,38,100)[STORE]L1:Sum((L1<35)*36-34)
I think that should work.
Problem 6.49 in the text has an incorrect answer in the back. The set-up is correct:
P(F) * P(R|F) = P(F & R)
so .4 * .8 = 0.32
but the book says 0.032.
The answer 0.32 is correct. Everyone makes mistakes occasionally. We blame George.
Use the Force, Luke.
Have any more questions? POST THEM HERE!
Hmmmm. What good questions should I put on the test????
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