1. In a word, this is “Craps”, a dice game that Las Vegas makes billions on. Let

Question

1. In a word, this is “Craps”, a dice game that Las Vegas makes billions on. Let’s calculate some probabilities that show why the “House” ALWAYS wins. It’s all about the odds.

a. (already done) You throw two dice or one die twice and record the two numbers. Draw a TABLE that shows ALL the possible combinations of the two numbers, for example the top left box would be (1,1). You can write the sum of the two numbers in the box also (1 + 1) = 2. (You should have 36 boxes).

b. On your first toss of the two dice, IF they total 7 or 11 you win. BUT, if they total 2, 3 or 12 you lose. What are the two probabilities for these possibilities?

c. Let’s say none of these totals came up. Instead the totals were 4, 5, 6, 8, 9, 10. What is their total probability?

d. To win now on the next toss you must get that same total. BUT if you get the 2, 3, 12 OR a 7 OR 11, you lose. Let’s say you got an 8 on your first toss. What is the probability of getting and 8 on the next toss to win? What is the probability of getting a losing number?

Explanation / Answer

P(7 or 11) = (6/36) + 2/36 = 2/9

P(2 or 3 or12) = (1/36) + (2/36) +(1/36) = 1/9

Therefore the probability of winning is (2/9)

And the probability of losing is (1/9)

c.) P( none of these totals came up) = 1 - (2/9) - (1/9) = 2/3

d.) P( getting 8 on the second toss | 8 on the first toss)

= P( of getting an 8)

= 5/36

P(getting a losing number ) = 1 - (5/36) = 31/36

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