Question

In a lottery game, a player picks six numbers from 1 to 22. If the player matches all six numbers, they win 20,000 dollars. Otherwise, they lose $1.

What is the expected value of this game?

Answer 1

Total possible number of outcomes = C(24,6) [24 choose 6]

=24!/(6!18!)

= 134596

Out of which there is only one winning combination.

Therefore we conclude:

P(win 20000)=1/134596

P(lose 1)=134595/134596

and hence the expected value is:

20000*(1/134596)+(-1)*(134595/134596)

=-114595/134596

=-0.8514 (rounded to four places after decimal)

Explanation:

Hope this helped!