To find the probability of winning the jackpot in this lottery, we need to calculate the chances of two independent events:

1. Selecting the correct 2 numbers between 1 and 57.
2. Selecting the correct single number between 1 and 33.

Step 1: Probability of selecting 2 correct numbers between 1 and 57

The number of ways to choose 2 numbers from 57 is a combination, calculated as:

$\binom{57}{2} = \frac{57 \times 56}{2!} = \frac{57 \times 56}{2} = 1,596$

So, there are 1,596 different ways to choose 2 numbers from 57.

The probability of selecting the 2 correct numbers is:

$P_1 = \frac{1}{\binom{57}{2}} = \frac{1}{1,596}$

Step 2: Probability of selecting the correct single number between 1 and 33

The probability of selecting the correct single number between 1 and 33 is:

$P_2 = \frac{1}{33}$

Step 3: Overall probability

Since these events are independent, we multiply the probabilities of each event:

$P_{\text{jackpot}} = P_1 \times P_2 = \frac{1}{1,596} \times \frac{1}{33} = \frac{1}{52,668}$

So, the probability of winning the jackpot is:

$P_{\text{jackpot}} = \frac{1}{52,668}$

Final Answer:

The probability of winning the jackpot is $\frac{1}{52,668}$, or approximately 0.00001898 (about 0.0019%).

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Would you like a detailed explanation of the combination formula or any part of this calculation?

Here are 5 follow-up questions:

1. How does the combination formula work in other scenarios?
2. What is the difference between independent and dependent events in probability?
3. How does the probability change if the range of numbers increases?
4. What are the odds of winning other lottery formats?
5. How can probability theory apply to real-life decision-making?

Tip: Always remember to account for whether events are independent or dependent when calculating joint probabilities!