Lot! Choose your numbers! Play a combination! But what are the odds of cashing in on the multi-million dollar prize?
Steps
Step 1. Identify the lottery rules
In this example you will choose 6 unique and different numbers from 1 to 50. You will win the prize if all 6 drawn numbers match yours - in any order.
Step 2. Create the 6 necessary factors:
- X1 = 6/50 = 0.12 (Probability that one of the 6 numbers is equal to one of yours)
- X2 = 5/49 = ~ 0.10 (Probability that one of the 5 remaining numbers is equal to your second number)
- X3 = 4/48 = 0.08 (Probability that one of the 4 remaining numbers is equal to your third number)
- X4 = 3/47 = ~ 0.06 (Probability that one of the 3 remaining numbers is equal to your fourth number)
- X5 = 2/46 = ~ 0.04 (Probability that one of the two remaining numbers is equal to your fifth number)
- X6 = 1/45 = 0.02 (Probability that the last number is equal to your sixth number)
Step 3. Multiply all the factors together:
X1 * X2 * X3 * X4 * X5 * X6 = ~ 0.0000000629 (this is the probability of winning)
Step 4. Divide the answer into fractions to calculate the odds against you
You have a 1 in 15,890,700 chance of winning.
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1 / 0.0000000629 = 15, 890, 700
Method 1 of 1: Calculate with a Wild Number
Step 1. Again, consider the rules
In this example choose 5 unique and different numbers from 1 to 50, and for the sixth number, you can choose any number from 1 to 50, even the same as those already chosen.
Step 2. Create the first 5 necessary factors:
- X1 = 5/50 = 0.1 (Probability that one of the 5 numbers is equal to your first number)
- X2 = 4/49 = ~ 0.082 (Probability that one of the 2 remaining numbers is equal to your second number)
- X3 = 3/47 = ~ 0.063 (Probability that one of the 3 remaining numbers is equal to your third number)
- X4 = 2/47 = ~ 0.043 (Probability that one of the 2 remaining numbers is equal to your fourth number)
- X5 = 1/46 = ~ 0.022 (Probability that the remaining number equals your fifth number)
Step 3. Create the sixth factor (wildcard number)
X6 = 1/50 = 0.02 (Probability that your wild card number is equal to the number drawn from 50)
Step 4. Multiply all the factors together:
X1 * X2 * X3 * X4 * X5 * X6 = ~ 0.00000000977 (this is the probability of winning)
Step 5. Divide the answer into a fraction to calculate the odds against you
You have a one in 102,354,145 chance of winning.
Advice
- DO NOT believe the scams that offer certain ways to win. If someone really had a way to win, imagine how much that information might be worth.
- ANY series of numbers has EXACTLY the same chances of being drawn. 32-45-22-19-9-11 is no different from 1-2-3-4-5-6. The drawn spheres are completely random.
- You can improve your chances of winning by buying more tickets more often, but remember that the numbers are very large. To get to a 50% chance in the lottery of the second example, you would have to buy two tickets a week for 702,442 years and three consecutive months.
- The odds of being struck by lightning are estimated at 1 in 400,000, which means you are 200 times more likely to win the lottery than the first example.
- To apply this method to other lotteries you will need to change the number of possible numbers drawn (for example 50 to 90).
- Remember that the odds are almost non-existent!
Warnings
- Don't bet more than you can afford to lose.
- Buying a lottery ticket is good business only when the value of the win (minus expenses and taxes) exceeds the probability of winning. If the odds are one in 15,000,000 and the lottery only pays 4,000,000 times the ticket price, this is not a good choice.
- If you think you have a gambling problem, it probably does. You can find information in support groups for those with this problem.
