. In a lottery game, a player picks six numbers from 1 to 23. If the player matches all six numbers, they win 30,000 dollars. Otherwise, they lose $1. Find the expected value of this game.

Question

. In a lottery game, a player picks six numbers from 1 to 23. If the player matches all six numbers, they win 30,000 dollars. Otherwise, they lose $1. Find the expected value of this game.

Answer 1

There are ₂₃C₆ ways to pick 6 numbers from 23; the probability of any particular one is just shy of 1/100000.

Thus the expectation for winning is about $0.30 and losing very close to $1...the t total expectation is about -$0.70.

You can calculate the exact number by using the exact probability of picking the winning number stated in the first line of this answer.