Answer to Question #124609 in Statistics and Probability for Daniel Degrossa

Question

In a lottery game, a player picks six numbers from 1 to 27. If the player matches all six numbers, they win 50,000 dollars. Otherwise, they lose $1.

What is the expected value of this game? $

Answer 1

Solution:

E[X]=x₁p₁+x₂p₂

x₁=50000,

p₁=m/n, m=1, n=binomial(27,6)=27!/6!/21!=296010,

here binomial(27,6) is the binomial coefficient (²⁷₆).

p₁=1/296010,

x₂=-1,

p₂=1-p₁=1-1/296010=296009/296010.

E[X]=50000*1/296010+(-1)296009/296010=-82003/98670=-0.83...

Answer:

E[X]=-82003/98670=-0.83...