Question

A certain game involves tossing 3 fair coins, and it pays 8¢ for 3 heads, 3¢ for 2 heads, and 1¢ for 1 head. Is 3¢ a fair price to pay to play this game? That is, does the 3¢ cost to play make the game fair? What are the expected winnings for this game in cents?

Step 1

We have given,

A fair coin is tossed 3 times. So, we can have following outcomes

{H,H,H}

{H,H,T}

{H,T,H}

{H,T,T}

{T,H,H}

{T,H,T}

{T,T,H}

{T,T,T}

For three Heads,

P(E) = 1/8

For two heads,

P(E) = 3/8

For One head,

P(E) = 3/8

Step 2

It pays 8¢ for 3 heads, 3¢ for 2 heads, and 1¢ for 1 head

We need to find expected value for this game

Step 3

Expected Value =

...

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