At a bazaar you can flip a fair coin until the first tail ap

At a bazaar you can flip a fair coin until the first tail appears. Your payoff is as follows:

If a tail appears on the first toss, you win $2

If a tail appears on the second toss, you win $4

If a tail appears on the third toss, you win $8

Compute the fair price to pay for this game is you will quit on the third toss, win or lose?

Solution

When we toss a coin then as we get one tail {T} the second toss can give {T,H} and similarly the third toss can give {T,H}

The sample space is {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT} with probability being 1/8

The summation of the expectation is the fair price of the sample =$3

The quitting of the game depends on the cost of playing the game here it is not given ,so if there is a profit then we can play the game if there is a loss then we shoulf not play