Question

Lottery: You enter a lottery by purchasing one of the 500 tickets. There is 1 grand prize winner, 3 second prize winners, and 12 small prize winners. These are selected at random from a bin containing all the tickets.

(a) What is the probability that you will win the grand prize? Express your answer as an exact decimal (not a percent and do not round).


(b) What is the probability that you will win a prize of some type? Express your answer as an exact decimal (not a percent and do not round).

Answer 1

One can buy one ticket from the 500 tickets in ⁵⁰⁰C₁=500 possible ways.

Given, there is 1 grand prize ticket, 3 second prize tickets and 12 small prize tickets.

a) Now, one can select a grand prize ticket in ¹C₁=1 possible way.

Thus, probability that one will win the grand prize is, 1/500=0.002.

b) The probability that one will win a prize of some type

=P(one will win a grand prize one will win the second prize one will win a small prize)

=P(one will win a grand prize ) +P(one will win the second prize) +P(one will win a small prize) [since the events are mutually exclusive]

=(¹C₁/500) +(³C₁/500) +(¹²C₁/500)

=0.032

Thus, the probability that one will win a prize of some type is 0.032.