Question

A certain game involves tossing 3 fair​ coins, and it pays 18cents for 3​ heads, 6cents for 2​ heads, and 2cents for 1 head. Is 6cents a fair price to pay to play this​ game? That​ is, does the 6cents cost to play make the game​ fair?

Answer 1

A fair price for this game would be 5.25 cents.

So this is not fair game

Explanation:

`\textrm{Probability of getting 2 heads}=(3)/(8)\\\textrm{Probability of getting 1 heads}=(3)/(8)\\\textrm{Probability of getting 3 heads}= \left((1)/(2)\right)^3=(1)/(8)`

`\textrm{Expected earnings} = (1)/(8)(\textrm{18 cents})+(3)/(8)(\textrm{6 cents}) + (3)/(8)(\textrm{2 cents})`

=5.25 cents

A fair price for this game would be 5.25 cents.

So this is not fair game