Probability question

Question

A lottery offers three prizes: $100, with a win probability of 1/200, $50, with a win probability of 1/100, and $11, with a win probability of 1/2. A single ticket cost $10.

what is the probability you win some kind of prize?

Answer 1

Since you are only asked the probability of any prize, the values of the prizes and the cost of the tickets are not important. Those would be used for determining the expected return, but you are not asked for that.

Each of the prizes is independent of each other, and winning any one of them satisfies the condition of having a winning ticket, so you can get the overall probability by adding the probability of winning each type of prize

P(first prize = 1/200

P(second prize) = 1/100

P(third prize) = 1/2

Adding these gives 1/200 + 1/100 + 1/2

Converting the denominators to 200:

1/200 + 2/200 + 100/200 = 103/200

p = 0.515

Hope this helps