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Class-Of-4-19 - R B R B R R B R R B R R B B R R R B R B R R...

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COMPUTING CONDITIONAL PROBABILITIES PROBABILITIES and EXPECTATIONS
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LET US PLAY A GAME You cast the dice try to get at least a 6 and later on an 8 before 7 comes up two times or at least an 8 and later on a 6 If you succeed you win!!! What is the probability of winning? 7 We will use the diagram in the next page to compute this probability next
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The game simulated by by three spins next PROBLEM: COMPUTE THE PROBABILITY OF WINNING AT THIS GAME
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Some suggestions for the next Quiz - label each problem clearly -write up your solutions to the problems in the original order - DO NOT show work on actual quiz sheet - DO NOT use red ink - print your name at the top right corner (on every sheet if no stapler) On the next Quiz, in addition to more decryption encryption, expect a problem such as this next
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The SAY RED card game
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B R B B R B R B B
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Unformatted text preview: R B R B R R B R R B R R B B R R R B R B R R R B B next RBRBB RRBBB R B R B R R B R R B R R B B R R R B R B R R R B B Winning cases Losing cases B RBB B RBB next The general case (*) Q E D ! KENO EXPECTATIONS The player marks n spots (chooses k numbers of the card) The house choses 20 distinct numbers from 1 to 80 Payoffs vary from house to house Here are two schedules What do you expect to win if you bet one dollar here ? What do you expect to win if you bet 5 dollars here ? ( n k )( 80-n 20-k ) ( 80 20 ) And what if you bet 1 dollar? Some interesting Answers = = = = /5 = In each case you should expect to lose about 27 cents per dollar!!! betting 5 dollars speeds up the process So you see that the craps game where you lose 2 cents per dollar is a bargain by comparison...
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