Question

.The probability of a $2 winner in a particular state lottery is 1 in 10, the probability of a $5 winner is 1 in 50, and the probability of a $10 winner is 1 in 500.

a) What is the probability of getting either a $2, or $5, or $10 winner? _____

b) What is the probability of getting a $2 winner? _____

c) If you buy 50 lottery tickets, what is the probability that you will get at least one $5 winner? _____

d) If you buy 500 lottery tickets, what is the probability that you will get at least one $10 winner? _____

Answer 1

a) What is the probability of getting either a $2, or $5, or $10 winner?

P($2)+P($5)+P($10) = 0.1+0.02+0.002 = 0.122

b) What is the probability of getting a $2 winner?

= 1/10 = 0.1

c) If you buy 50 lottery tickets, what is the probability that you will get at least one $5 winner?

P(atleast 1 $5) = 1 - P(no $5 ticket out of 50) = 1 - [(1-0.02)^50] = 0.6358

d) If you buy 500 lottery tickets, what is the probability that you will get at least one $10 winner?

P(atleast 1 $10) = 1 - P(no $10 ticket out of 500) = 1 - [(1-0.002)^500] = 0.6325