The Sorry State Lottery requires you to select 7 different numbers from 0 through 55. (Order is not important.) You are a Big Winner if the 7 numbers you select agree with those in the drawing, and you are a Small-Fry Winner if 6 of your 7 numbers agree with those in the drawing. (Round all answers to three significant figures. Enter the answers in scientific notation.)

What is the probability of being a Big Winner?

What is the probability of being a Small-Fry Winner?

What is the probability that you are either a Big Winner or a Small-Fry winner?

The probability of picking the first number correctly is 1/56, since zero is included. Since the numbers are not replaced, the probability of the second is 1/55, the third, 1/54 and so on.

The probability of all events occurring is obtained by multiplying the individual probabilities.

The probability of either one event or another occurring is found by adding the probability of the individual events.

I hope this helps. Thanks for asking.

To find the probabilities of being a Big Winner, Small-Fry Winner, and the probability of being either a Big Winner or a Small-Fry winner, we need to calculate the number of possible winning combinations and divide it by the total number of possible combinations.

1. Probability of being a Big Winner:
To be a Big Winner, we need to select all 7 correct numbers from the pool of 0 through 55. Since order does not matter, this is a combination problem. The number of ways to choose 7 numbers from a pool of 56 (0 through 55) is calculated using the combination formula:

C(n, r) = n! / (r! * (n-r)!)

In this case, n = 56 (total numbers in the pool) and r = 7 (numbers to be chosen).

So, the number of possible Big Winner combinations is:
C(56, 7) = 56! / (7! * (56-7)!)

Now, we need to find the total number of combinations possible when selecting 7 numbers from the pool of 0 through 55, which is C(56, 7).

The probability of being a Big Winner is the number of possible Big Winner combinations divided by the total number of combinations:

Probability of being a Big Winner = C(56, 7) / C(56, 7)

2. Probability of being a Small-Fry Winner:
To be a Small-Fry Winner, we need to select 6 correct numbers out of the 7 numbers selected in the drawing, and one number that is not selected. Again, this is a combination problem. The number of ways to choose 6 numbers out of the 7 selected in the drawing is:

C(7, 6) = 7! / (6! * (7-6)!)

The additional number that is not selected can be any of the remaining 49 numbers from the pool (56 - 7 = 49).

So, the number of possible Small-Fry Winner combinations is:
C(7, 6) * 49 = (7! / (6! * (7-6)!)) * 49

The total number of combinations possible when selecting 7 numbers from the pool of 0 through 55 is the same as before, C(56, 7).

The probability of being a Small-Fry Winner is the number of possible Small-Fry Winner combinations divided by the total number of combinations:

Probability of being a Small-Fry Winner = (C(7, 6) * 49) / C(56, 7)

3. Probability of being either a Big Winner or a Small-Fry Winner:
To find the probability of being either a Big Winner or a Small-Fry Winner, we add the probabilities of being a Big Winner and a Small-Fry Winner:

Probability of being either a Big Winner or a Small-Fry Winner = Probability of being a Big Winner + Probability of being a Small-Fry Winner

Please note that you need to calculate the probabilities using the provided formulas with the actual values for n and r, then round the answers to three significant figures and express them in scientific notation.