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

Answer:

A fair price for this game would be 5.25 cents.

So this is not fair game

Step-by-step explanation:

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

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

=5.25 cents

A fair price for this game would be 5.25 cents.

So this is not fair game