In the power ball lottery game, winning the jackpot requires that you select the correct five unique numbers between 1 and 58 inclusive (don't have to match the order) and, in a separate drawing, you must also select the correct single nber between 1 and 13 inclusive. Find the probability of winning the jackpot?
To find the probability of winning the jackpot in the Powerball lottery game, we need to calculate the total number of possible outcomes and the number of favorable outcomes.
1. Calculate the total number of possible outcomes:
In the first drawing for the unique numbers between 1 and 58, there are 58 options for the first number, 57 options for the second number, 56 options for the third number, and so on until the fifth number, which has 54 options. So, the total number of options for the unique numbers is calculated as:
58 * 57 * 56 * 55 * 54 = 66,474,840
In the second drawing for the single number between 1 and 13, there are 13 options.
Therefore, the total number of possible outcomes is:
66,474,840 * 13 = 864,345,120
2. Calculate the number of favorable outcomes:
To win the jackpot, you need to select the correct unique numbers and the correct single number. There is only 1 favorable outcome for both parts.
3. Calculate the probability:
The probability of winning the jackpot is the ratio of the number of favorable outcomes to the total number of possible outcomes. So, the probability is:
1 / 864,345,120 ≈ 0.00000000116
Therefore, the probability of winning the jackpot in the Powerball lottery game is approximately 0.00000000116 or 1 in 864,345,120.
virtually zero.
since there is no replacement between draws,
1st # 1/58
2nd # 1/57
...
and so on
multiply them all together