Question

A lottery ticket is given. For this lottery, five integer numbers are chosen from 1 to 50, and the order doesn’t matter. You win the main prize of one million dollars if your ticket matches all five numbers drawn; you win a second prize of one thousand dollars if your ticket matches exactly four of the five numbers drawn; and otherwise you win nothing.

a. What’s the probability that you win the main prize?

b. What’s the probability that you win something of positive value?

c. Let X be the amount of money you win. What’s the expected value of X? Write it as an expression that is the sum of three terms.

d. What’s the variance of X? Write it as the sum of three terms, where you can simply write “E(X)” for the expected value within your expression.

Answer 1