Lottery Odds worksheet

1. Jackpot odds (1 in …): 1,501,915,800

1. Count the ways to pick 6 of 60 main numbers. Order doesn't matter, so this is a combination: C(60, 6) = 60! ÷ (6! × 54!)

   $\text{C(60, 6)}$$=\mathrm{50,063,860}$

2. Multiply by the 30 possible bonus balls, because each main set can pair with any of them. This gives the number of different tickets

   $\mathrm{50,063,860}\times 30$$=\mathrm{1,501,915,800}$

3. Only one ticket matches everything, so the jackpot odds are 1 in that many tickets

   $\text{P(jackpot) = 1 ÷}$$=\mathrm{1,501,915,800}$$=\text{≈}$$=\mathrm{0.0000000666\%}$

4. Find what one ticket gets back from the jackpot on average: the jackpot × its chance. This ignores smaller prizes, taxes and shared jackpots

   $\frac{\mathrm{\$76,000,000.00}}{\mathrm{1,501,915,800}}$$=\mathrm{\$0.05}$

5. Subtract the ticket price to see the average gain or loss per ticket from the jackpot alone

   $\mathrm{\$0.05}-\mathrm{\$2.00}$$=\mathrm{-\$1.95}$

6. Jackpot odds

   $\text{1 in}\mathrm{1,501,915,800}$

2. Jackpot odds (1 in …): 42,493,374

1. Count the ways to pick 5 of 46 main numbers. Order doesn't matter, so this is a combination: C(46, 5) = 46! ÷ (5! × 41!)

   $\text{C(46, 5)}$$=\mathrm{1,370,754}$

2. Multiply by the 31 possible bonus balls, because each main set can pair with any of them. This gives the number of different tickets

   $\mathrm{1,370,754}\times 31$$=\mathrm{42,493,374}$

3. Only one ticket matches everything, so the jackpot odds are 1 in that many tickets

   $\text{P(jackpot) = 1 ÷}$$=\mathrm{42,493,374}$$=\text{≈}$$=\mathrm{0.0000023533\%}$

4. Find what one ticket gets back from the jackpot on average: the jackpot × its chance. This ignores smaller prizes, taxes and shared jackpots

   $\frac{\mathrm{\$120,000,000.00}}{\mathrm{42,493,374}}$$=\mathrm{\$2.82}$

5. Subtract the ticket price to see the average gain or loss per ticket from the jackpot alone

   $\mathrm{\$2.82}-\mathrm{\$2.00}$$=\mathrm{\$0.82}$

6. Jackpot odds

   $\text{1 in}\mathrm{42,493,374}$

3. Jackpot odds (1 in …): 9,549,540

1. Count the ways to pick 4 of 55 main numbers. Order doesn't matter, so this is a combination: C(55, 4) = 55! ÷ (4! × 51!)

   $\text{C(55, 4)}$$=\mathrm{341,055}$

2. Multiply by the 28 possible bonus balls, because each main set can pair with any of them. This gives the number of different tickets

   $\mathrm{341,055}\times 28$$=\mathrm{9,549,540}$

3. Only one ticket matches everything, so the jackpot odds are 1 in that many tickets

   $\text{P(jackpot) = 1 ÷}$$=\mathrm{9,549,540}$$=\text{≈}$$=\mathrm{0.0000104717\%}$

4. Find what one ticket gets back from the jackpot on average: the jackpot × its chance. This ignores smaller prizes, taxes and shared jackpots

   $\frac{\mathrm{\$100,000,000.00}}{\mathrm{9,549,540}}$$=\mathrm{\$10.47}$

5. Subtract the ticket price to see the average gain or loss per ticket from the jackpot alone

   $\mathrm{\$10.47}-\mathrm{\$3.00}$$=\mathrm{\$7.47}$

6. Jackpot odds

   $\text{1 in}\mathrm{9,549,540}$

4. Jackpot odds (1 in …): 9,015,006,000

1. Count the ways to pick 6 of 80 main numbers. Order doesn't matter, so this is a combination: C(80, 6) = 80! ÷ (6! × 74!)

   $\text{C(80, 6)}$$=\mathrm{300,500,200}$

2. Multiply by the 30 possible bonus balls, because each main set can pair with any of them. This gives the number of different tickets

   $\mathrm{300,500,200}\times 30$$=\mathrm{9,015,006,000}$

3. Only one ticket matches everything, so the jackpot odds are 1 in that many tickets

   $\text{P(jackpot) = 1 ÷}$$=\mathrm{9,015,006,000}$$=\text{≈}$$=\mathrm{0.0000000111\%}$

4. Find what one ticket gets back from the jackpot on average: the jackpot × its chance. This ignores smaller prizes, taxes and shared jackpots

   $\frac{\mathrm{\$122,500,000.00}}{\mathrm{9,015,006,000}}$$=\mathrm{\$0.01}$

5. Subtract the ticket price to see the average gain or loss per ticket from the jackpot alone

   $\mathrm{\$0.01}-\mathrm{\$2.00}$$=\mathrm{-\$1.99}$

6. Jackpot odds

   $\text{1 in}\mathrm{9,015,006,000}$

5. Jackpot odds (1 in …): 4,816,520,436

1. Count the ways to pick 6 of 74 main numbers. Order doesn't matter, so this is a combination: C(74, 6) = 74! ÷ (6! × 68!)

   $\text{C(74, 6)}$$=\mathrm{185,250,786}$

2. Multiply by the 26 possible bonus balls, because each main set can pair with any of them. This gives the number of different tickets

   $\mathrm{185,250,786}\times 26$$=\mathrm{4,816,520,436}$

3. Only one ticket matches everything, so the jackpot odds are 1 in that many tickets

   $\text{P(jackpot) = 1 ÷}$$=\mathrm{4,816,520,436}$$=\text{≈}$$=\mathrm{0.0000000208\%}$

4. Find what one ticket gets back from the jackpot on average: the jackpot × its chance. This ignores smaller prizes, taxes and shared jackpots

   $\frac{\mathrm{\$100,000,000.00}}{\mathrm{4,816,520,436}}$$=\mathrm{\$0.02}$

5. Subtract the ticket price to see the average gain or loss per ticket from the jackpot alone

   $\mathrm{\$0.02}-\mathrm{\$1.00}$$=\mathrm{-\$0.98}$

6. Jackpot odds

   $\text{1 in}\mathrm{4,816,520,436}$

6. Jackpot odds (1 in …): 239,536,752

1. Count the ways to pick 5 of 65 main numbers. Order doesn't matter, so this is a combination: C(65, 5) = 65! ÷ (5! × 60!)

   $\text{C(65, 5)}$$=\mathrm{8,259,888}$

2. Multiply by the 29 possible bonus balls, because each main set can pair with any of them. This gives the number of different tickets

   $\mathrm{8,259,888}\times 29$$=\mathrm{239,536,752}$

3. Only one ticket matches everything, so the jackpot odds are 1 in that many tickets

   $\text{P(jackpot) = 1 ÷}$$=\mathrm{239,536,752}$$=\text{≈}$$=\mathrm{0.0000004175\%}$

4. Find what one ticket gets back from the jackpot on average: the jackpot × its chance. This ignores smaller prizes, taxes and shared jackpots

   $\frac{\mathrm{\$90,000,000.00}}{\mathrm{239,536,752}}$$=\mathrm{\$0.38}$

5. Subtract the ticket price to see the average gain or loss per ticket from the jackpot alone

   $\mathrm{\$0.38}-\mathrm{\$2.00}$$=\mathrm{-\$1.62}$

6. Jackpot odds

   $\text{1 in}\mathrm{239,536,752}$

7. Jackpot odds (1 in …): 43,304,800

1. Count the ways to pick 4 of 77 main numbers. Order doesn't matter, so this is a combination: C(77, 4) = 77! ÷ (4! × 73!)

   $\text{C(77, 4)}$$=\mathrm{1,353,275}$

2. Multiply by the 32 possible bonus balls, because each main set can pair with any of them. This gives the number of different tickets

   $\mathrm{1,353,275}\times 32$$=\mathrm{43,304,800}$

3. Only one ticket matches everything, so the jackpot odds are 1 in that many tickets

   $\text{P(jackpot) = 1 ÷}$$=\mathrm{43,304,800}$$=\text{≈}$$=\mathrm{0.0000023092\%}$

4. Find what one ticket gets back from the jackpot on average: the jackpot × its chance. This ignores smaller prizes, taxes and shared jackpots

   $\frac{\mathrm{\$100,000,000.00}}{\mathrm{43,304,800}}$$=\mathrm{\$2.31}$

5. Subtract the ticket price to see the average gain or loss per ticket from the jackpot alone

   $\mathrm{\$2.31}-\mathrm{\$2.00}$$=\mathrm{\$0.31}$

6. Jackpot odds

   $\text{1 in}\mathrm{43,304,800}$

8. Jackpot odds (1 in …): 250,179,072

1. Count the ways to pick 5 of 68 main numbers. Order doesn't matter, so this is a combination: C(68, 5) = 68! ÷ (5! × 63!)

   $\text{C(68, 5)}$$=\mathrm{10,424,128}$

2. Multiply by the 24 possible bonus balls, because each main set can pair with any of them. This gives the number of different tickets

   $\mathrm{10,424,128}\times 24$$=\mathrm{250,179,072}$

3. Only one ticket matches everything, so the jackpot odds are 1 in that many tickets

   $\text{P(jackpot) = 1 ÷}$$=\mathrm{250,179,072}$$=\text{≈}$$=\mathrm{0.0000003997\%}$

4. Find what one ticket gets back from the jackpot on average: the jackpot × its chance. This ignores smaller prizes, taxes and shared jackpots

   $\frac{\mathrm{\$105,000,000.00}}{\mathrm{250,179,072}}$$=\mathrm{\$0.42}$

5. Subtract the ticket price to see the average gain or loss per ticket from the jackpot alone

   $\mathrm{\$0.42}-\mathrm{\$2.00}$$=\mathrm{-\$1.58}$

6. Jackpot odds

   $\text{1 in}\mathrm{250,179,072}$

9. Jackpot odds (1 in …): 8,185,320

1. Count the ways to pick 4 of 55 main numbers. Order doesn't matter, so this is a combination: C(55, 4) = 55! ÷ (4! × 51!)

   $\text{C(55, 4)}$$=\mathrm{341,055}$

2. Multiply by the 24 possible bonus balls, because each main set can pair with any of them. This gives the number of different tickets

   $\mathrm{341,055}\times 24$$=\mathrm{8,185,320}$

3. Only one ticket matches everything, so the jackpot odds are 1 in that many tickets

   $\text{P(jackpot) = 1 ÷}$$=\mathrm{8,185,320}$$=\text{≈}$$=\mathrm{0.000012217\%}$

4. Find what one ticket gets back from the jackpot on average: the jackpot × its chance. This ignores smaller prizes, taxes and shared jackpots

   $\frac{\mathrm{\$100,000,000.00}}{\mathrm{8,185,320}}$$=\mathrm{\$12.22}$

5. Subtract the ticket price to see the average gain or loss per ticket from the jackpot alone

   $\mathrm{\$12.22}-\mathrm{\$2.00}$$=\mathrm{\$10.22}$

6. Jackpot odds

   $\text{1 in}\mathrm{8,185,320}$

10. Jackpot odds (1 in …): 1,051,341,060

1. Count the ways to pick 6 of 60 main numbers. Order doesn't matter, so this is a combination: C(60, 6) = 60! ÷ (6! × 54!)

   $\text{C(60, 6)}$$=\mathrm{50,063,860}$

2. Multiply by the 21 possible bonus balls, because each main set can pair with any of them. This gives the number of different tickets

   $\mathrm{50,063,860}\times 21$$=\mathrm{1,051,341,060}$

3. Only one ticket matches everything, so the jackpot odds are 1 in that many tickets

   $\text{P(jackpot) = 1 ÷}$$=\mathrm{1,051,341,060}$$=\text{≈}$$=\mathrm{0.0000000951\%}$

4. Find what one ticket gets back from the jackpot on average: the jackpot × its chance. This ignores smaller prizes, taxes and shared jackpots

   $\frac{\mathrm{\$105,000,000.00}}{\mathrm{1,051,341,060}}$$=\mathrm{\$0.10}$

5. Subtract the ticket price to see the average gain or loss per ticket from the jackpot alone

   $\mathrm{\$0.10}-\mathrm{\$3.00}$$=\mathrm{-\$2.90}$

6. Jackpot odds

   $\text{1 in}\mathrm{1,051,341,060}$