Winning the jackpot in a particular lottery requires that you select the correct two numbers between 1 and 56 and, in a separate drawing, you must also select the correct single number between 1 and 59. Find the probability of winning the jackpot.

If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.

1/56 * 1/(56-1) * 1/59 = ?

To find the probability of winning the jackpot, we need to calculate the probability of selecting the correct two numbers between 1 and 56 and the correct single number between 1 and 59.

The probability of selecting the correct two numbers between 1 and 56 can be calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes.

The number of favorable outcomes is 1, as there is only one winning combination for the two numbers.

The total number of possible outcomes is given by the product of the number of choices for each number. Since there are 56 choices for the first number and 55 choices for the second number (since repetition is not allowed), the total number of possible outcomes is 56 * 55.

Therefore, the probability of selecting the correct two numbers is 1 / (56 * 55).

Now, let's calculate the probability of selecting the correct single number between 1 and 59.

The probability of selecting the correct single number is 1 out of 59, as there is only one winning number.

Therefore, the probability of selecting the correct single number is 1 / 59.

To calculate the probability of winning the jackpot, we multiply the probabilities of selecting the correct two numbers and the correct single number.

Probability of winning the jackpot = (1 / (56 * 55)) * (1 / 59).

Now, we can evaluate this expression to find the exact probability.

To find the probability of winning the jackpot, we need to determine the number of possible winning outcomes (successful outcomes) and the total number of possible outcomes (sample space).

Step 1: Determine the number of possible outcomes for each component of the winning numbers.

For the first drawing, you need to select any two numbers between 1 and 56. This can be calculated using the combination formula, which is "nCr" where n is the total number of items and r is the number of items to be selected without replacement.

The number of possible combinations for selecting two numbers out of 56 is given by:

56C2 = (56!)/(2!(56-2)!) = (56!)/(2!54!) = (56 x 55)/(2 x 1) = 56 x 55 / 2 = 1540

So, there are 1540 possible outcomes for the first part of the winning numbers.

For the second drawing, you need to select a single number between 1 and 59. This can be calculated using the permutation formula, which is "nPr" where n is the total number of items and r is the number of items to be selected without replacement.

The number of possible permutations for selecting one number out of 59 is given by:

59P1 = 59!/(1!(59-1)!) = 59

So, there are 59 possible outcomes for the second part of the winning numbers.

Step 2: Determine the total number of possible outcomes for the entire jackpot.

Since each of the two drawings is independent, we can multiply the number of outcomes for each drawing to get the total number of outcomes for the entire jackpot.

Total outcomes = Number of outcomes for the first drawing x Number of outcomes for the second drawing
Total outcomes = 1540 x 59 = 90860

Therefore, there are 90860 possible outcomes for the entire jackpot.

Step 3: Calculate the probability of winning the jackpot.

The probability of winning is given by the number of successful outcomes divided by the total number of possible outcomes.

Number of successful outcomes = 1 (since there is only one winning combination)

Probability = Number of successful outcomes / Total number of possible outcomes
Probability = 1 / 90860

Hence, the probability of winning the jackpot is 1 in 90860.