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Mega Millions Lottery ~ Calculate Odds

Jackpot probability/odds (Payout varies)

The number of ways the first 5 numbers on your lottery ticket can match the 5 White numbers is COMBIN(5,5) = 1. The number of ways your final number can match the Mega number is: COMBIN(1,1) = 1. The product of these is the number of ways you can win the Jackpot:  COMBIN(5,5) x COMBIN(1,1) = 1. The probability of success is thus: 1/175,711,536 = 0.00000000569114597006. If you express this as "One chance in ???", you just divide "1" by the . 00000000569114597006, which yields "One chance in 175,711,536”.

Match all 5 White numbers but not the Mega number (Payout = $250,000)

The number of ways the 5 first numbers on your lottery ticket can match the 5 White numbers is COMBIN(5,5) = 1. The number of ways your final number can match any of the 45 losing Mega numbers is: COMBIN(45,1) = 45. (Pick any of the 45 losers.) Thus there are COMBIN(5,5) x COMBIN(45,1) = 45 possible combinations. The probability for winning $250,000 is thus 45/175,711,536 = .000000256101568653 or "One chance in 3,904,700.80".

Match 4 out of 5 White numbers and match the Mega number (Payout = $10,000)

The number of ways 4 of the 5 first numbers on your lottery ticket can match the 5 White numbers is COMBIN(5,4) = 5. The number of ways your fifth initial number can match any of the 51 losing White numbers is COMBIN(51,1) = 51.  The number of ways your final number can match the Mega number is: COMBIN(1,1) = 1. The product of these is the number of ways you can win this configuration:  COMBIN(5,4) x COMBIN(51,1) x COMBIN(1,1) = 255. The probability of success is thus: 255/175,711,536  = 0.00000145124222237 or "One chance in 689,064.85".

Match 4 out of 5 White numbers but not match the Mega number (Payout = $150)

The number of ways 4 of the 5 first numbers on your lottery ticket can match the 5 White numbers is COMBIN(5,4) = 5. The number of ways your fifth initial number can match any of the 51 losing White numbers is COMBIN(51,1) = 51.  The number of ways your final number can match any of the 45 losing Mega numbers is: COMBIN(45,1) = 45. The product of these is the number of ways you can win this configuration:  COMBIN(5,4) x COMBIN(51,1) x COMBIN(45,1) = 11,475. The probability of success is thus: 11,475/175,711,536 = 0.0000653059000065 or "One chance in 15,312.55".

Match 3 out of 5 White numbers and match the Mega number (Payout = $150)

The number of ways 3 of the 5 first numbers on your lottery ticket can match the 5 White numbers is COMBIN(5,3) = 10. The number of ways the 2 losing initial numbers on your ticket can match any of the 51 losing White numbers is COMBIN(51,2) = 1,275.  The number of ways your final number can match the Mega number is: COMBIN(1,1) = 1. The product of these is the number of ways you can win this configuration:  COMBIN(5,3) x COMBIN(51,2) x COMBIN(1,1) = 12,750. The probability of success is thus: 12,750/175,711,536 = 0.0000725621111183 or "One chance in 13,781.30".

Match 3 out of 5 White numbers but not match the Mega number (Payout = $7)

The number of ways 3 of the 5 first numbers on your lottery ticket can match the 5 White numbers is COMBIN(5,3) = 10. The number of ways the 2 losing initial numbers on your ticket can match any of the 51 losing White numbers is COMBIN(51,2) = 1,275.  The number of ways your final number can match any of the 45 losing Mega numbers is: COMBIN(45,1) = 45. The product of these is the number of ways you can win this configuration:  COMBIN(5,3) x COMBIN(51,2) x COMBIN(45,1) = 573,750. The probability of success is thus: 573,750/175,711,536 = 0.00326529500032 or "One chance in 306.25".

Match 2 out of 5 White numbers and match the Mega number (Payout = $10)

The number of ways 2 of the 5 first numbers on your lottery ticket can match the 5 White numbers is COMBIN(5,2) = 10. The number of ways the 3 losing initial numbers on your ticket can match any of the 51 losing White numbers is COMBIN(51,3) = 20,825.  The number of ways your final number can match the Mega number is: COMBIN(1,1) = 1. The product of these is the number of ways you can win this configuration:  COMBIN(5,2) x COMBIN(51,3) x COMBIN(1,1) = 208,250. The probability of success is thus: 208,250/175,711,536 = 0.00118518114827 or "One chance in 843.75".

Match 1 out of 5 White numbers and match the Mega number (Payout = $3)

The number of ways 1 of the 5 first numbers on your lottery ticket can match the 5 White numbers is COMBIN(5,1) = 5. The number of ways the 4 losing initial numbers on your ticket can match any of the 51 losing White numbers is COMBIN(51,4) = 249,900.  The number of ways your final number can match the Mega number is: COMBIN(1,1) = 1. The product of these is the number of ways you can win this configuration:  COMBIN(5,1) x COMBIN(51,4) x COMBIN(1,1) = 1,249,500. The probability of success is thus: 1,249,500/175,711,536 = 0.00711108688959 or "One chance in 140.63".

Match 0 out of 5 White numbers and match the Mega number (Payout = $2)

The number of ways 0 of the 5 first numbers on your lottery ticket can match the 5 White numbers is COMBIN(5,0) = 1. The number of ways the 5 losing initial numbers on your ticket can match any of the 51 losing White numbers is COMBIN(51,5) = 2,349,060.  The number of ways your final number can match the Mega number is: COMBIN(1,1) = 1. The product of these is the number of ways you can win this configuration:  COMBIN(5,0) x COMBIN(51,5) x COMBIN(1,1) = 2,349,060. The probability of success is thus: 2,349,060/175,711,536 = 0.0133688433524 or "One chance in 74.80".

Probability of winning something

If we add all the ways you can win something we get:
1 + 45 + 255 + 11,475 + 12,750 + 573,750 + 208,250 + 1,249,500 + 2,349,060 = 4,405,086 different ways of winning something. If we divide by the 175,711,536, we get .0250699874367 as a probability of winning something.  1 divided by 0.0250699874367 yields "One chance in 39.89" of winning something.

We thank http://www.durangobill.com/MegaMillionsOdds.html for the odds calculation results. Visit his page for the mathamatical calculations.

 

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