The Sorry State Lottery requires you to select five differen

The Sorry State Lottery requires you to select five different numbers from 0 through 66. (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?

Solution

Number of numbers = 67 (1 + 66, since 0 is included in the lot)

Probability of being a big winner = 5C5/67C5 = 1/9657648 = 1.03544 * 10^(-7)

Probability of being a small winner = (5C4 * 48C1)/67C5 = 0.00002485077

Probability of big winner or small winner = P(big winner) + P(small winner) = 1/67C5 + 240/67C5 = 241/67C5 = 241/9657648