Journal%2DErtry%2012am 1Compatitity Model-Word syout References Mailings Review
ID: 3361831 • Letter: J
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Journal%2DErtry%2012am 1Compatitity Model-Word syout References Mailings Review View 9 The winning Powerball ticket is a string of S numbers and then a Powerball number For example, the winning ticket on 11/4/2015 was 2-12-17-20-65-Powerball: 17 You win an amount based on how many numbers you have in common with the winning ticket (So the order of the numbers on your ticket doesn't matter.) Number 5 of 5 wPowerball 5 of 5 4 of 5 Amount $142 Mllor $1000.000 4 of5 wiPower $10,000 100 Let's compute the expected value of playing the Texas Lottery Powerball How many total possible options are there for the winning ticket? probability of winning the $142 Million.) the probability of winning $1.000,000.) probablity of winning $10,000.) 1. 2. What is the probability of matching 5 of S AND the powerball? (This is the 3. What is the probability of matching 5 of 5 but NOT matching the poeball (This 4. What is the probablity of matching exactly 4 of S AND the goerball (This is the 5. What is the probability of matching exactly 4 of S but NOT the powerball CThis isExplanation / Answer
Assuming numbers on the lottery ticket are between 0 and 99.
1.
Number of powerball winning tickets = 5!*1 = 120 . (Since order doesn't matter and powerball number has to match)
Number of 5 out of 5 matching tickets without powerball = 5!*99 = 11880 (Since order doesn't matter and powerball number has to not match)
Number of 4 out of 5 matching tickets with powerball = 5C4*99*5! = 5*99*120 = 59400
Number of 4 out of 5 matching tickets without powerball = 5C4*99*5!*99 = 5880600
2.
Total number of tickets possible = 100*100*100*100*100*100 = 1012
Probability of powerball winning tickets = No. of powerball tickets/Total number of tickets
= 120/1012 = 0.00000000012
3.
Similarly,
Probability of 5 out of 5 matching tickets without powerball = 11880/1012 = 0.00000001188
4.
Probability of 4 out of 5 matching tickets with powerball = 59400/1012 = 0.0000000594
5.
Probability of 4 out of 5 matching tickets without powerball = 5880600/1012 = 0.0000058806
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