Question

The Sorry State Lottery requires you to select five different numbers from 0 through 51 . (Order is not important.) You are a Big Winner if the five numbers you select agree with those in the drawing, and you are a Small-Fry Winner if four of your five numbers agree with those in the drawing. (Enter your answers as exact answers.) 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?

Answer 1

To calculate the probability of being a Big Winner, divide 1 by the total number of combinations. To calculate the probability of being a Small-Fry Winner, sum the probabilities of choosing 4 correct numbers and 1 incorrect number. To calculate the probability of being either a Big Winner or a Small-Fry Winner, add the probabilities of being a Big Winner and being a Small-Fry Winner.

Step-by-step explanation:

To calculate the probability of being a Big Winner, we need to consider that there are 52 numbers to choose from and we need to select 5 numbers. The order of the numbers does not matter, so we can use the combination formula. The probability of choosing all 5 correct numbers is the number of successful outcomes divided by the total number of possible outcomes. In this case, there is only one way to choose the correct 5 numbers out of 52. So, the probability of being a Big Winner is 1 divided by the total number of combinations.

To calculate the probability of being a Small-Fry Winner, we need to consider that there are 5 numbers to choose correctly and 47 numbers to choose incorrectly. Again, the order does not matter, so we can use the combination formula. The probability of choosing 4 correct numbers and 1 incorrect number is the number of successful outcomes divided by the total number of possible outcomes. There are 5 ways to choose 4 correct numbers and 47 ways to choose 1 incorrect number out of 52. So, the probability of being a Small-Fry Winner is the sum of these probabilities.

To calculate the probability of being either a Big Winner or a Small-Fry Winner, we need to add the probabilities of being a Big Winner and being a Small-Fry Winner.