Probability Lottery Question

Question

The Probability of a $1 winner in a particular state lottery is 1 in 8, the probability of a $5 winner is 1 in 100, and the probability of a $25 winner is 1 in 800.

a) What is the probability of getting either a $1, $5 or $25 winner?

b) If you buy 25 lottery tickets, what is the probability that you will get at least one $5 winner?

Answer 1

a) I'm assuming you can only win one prize per ticket, which means winning the various prizes are mutually exclusive events. So, to find the probability of winning a $1 prize or a $5 prize or a $25 prize, we can just add together the individual probabilities.

1/8 + 1/100 + 1/800 = 0.13625

b) P(at least 1 $5 winner) = 1 - P(no $5 winners) = 1 - (1-1/100)²⁵ ≈ 0.222