A lottery ticket contains 5 numbers chosen from the numbers 1 to 40. The winning ticket is the one that matches all the 5 numbers in the correct order. The second prize winner matches four of the five numbers in the correct order. What is the probability of winning the first or second prize?

To calculate the probability of winning the first or second prize in the lottery, we need to calculate the probability of winning the first prize and the probability of winning the second prize separately, and then add them together.

Probability of winning the first prize:
There is only one winning ticket with all five numbers in the correct order. So, the probability of winning the first prize is 1 out of the total possible outcomes, which is the total number of ways to choose 5 numbers out of 40.

The number of ways to choose 5 numbers out of 40 is given by the combination formula: C(40, 5) = 40! / (5! * (40-5)!) = 40! / (5! * 35!) = (40 * 39 * 38 * 37 * 36) / (5 * 4 * 3 * 2 * 1) = 658,008.

Therefore, the probability of winning the first prize is 1/658,008.

Probability of winning the second prize:
To win the second prize, the ticket must match four out of the five numbers in the correct order. There are 5 different positions where the one unmatched number can be placed. The remaining four positions can be filled with numbers that match the ticket.

The probability of matching the first number and not matching the remaining four numbers is (1/40) * (39/39) * (38/38) * (37/38) * (36/38).

The probability of matching the second number and not matching the remaining four numbers is (1/40) * (1/39) * (38/38) * (37/38) * (36/38).

Similarly, the probabilities for matching the third, fourth, and fifth numbers are (1/40) * (1/39) * (1/38) * (37/38) * (36/38), (1/40) * (1/39) * (1/38) * (1/37) * (36/38), and (1/40) * (1/39) * (1/38) * (1/37) * (1/36), respectively.

Since there are 5 different positions for the unmatched number, we need to multiply each of the above probabilities by 5.

Therefore, the probability of winning the second prize is (5 * [(1/40) * (39/39) * (38/38) * (37/38) * (36/38)]) = 5/19,600.

Final Probability:
To calculate the probability of winning the first or second prize, we simply add the probabilities together:

1/658,008 + 5/19,600 = 6/131,705.

Therefore, the probability of winning the first or second prize is 6/131,705.

To calculate the probability of winning the first or second prize, we need to determine the total number of possible outcomes and the number of favorable outcomes.

Total outcomes:
For each of the 5 numbers on the ticket, there are 40 possible numbers to choose from. Therefore, the total number of possible outcomes is 40^5 (40 raised to the power of 5), which equals 1,024,000,000.

First prize:
To win the first prize, all 5 numbers must be chosen correctly in the specific order. There is only one winning combination out of the 1,024,000,000 possible outcomes.

Second prize:
To win the second prize, four out of the five numbers must be chosen correctly in the specific order. The remaining fifth number can be any of the remaining 39 numbers. There are 5 different positions where the fifth number can be placed in the combination. So, the number of winning combinations is 1 * 5 * 39 = 195.

Probability:
The probability of an event occurring is the number of favorable outcomes divided by the number of possible outcomes.

For the first prize:
Probability of winning the first prize = 1 / 1,024,000,000

For the second prize:
Probability of winning the second prize = 195 / 1,024,000,000

To find the probability of winning either the first or second prize, you can add the probabilities together:

Total probability = (1 + 195) / 1,024,000,000

Therefore, the probability of winning the first or second prize is approximately 0.000000195, or 1.95 x 10^-7.

5 numbers = 1/40 * 1/39 * 1/38 * 1/37 *1/36 = ?

4 numbers = 1/40 * 1/39 * 1/38 * 1/37 = ?

Either-or probabilities are found by adding the individual probabilities.