in a game a player pays 1 and then tosses a fair coin until

in a game a player pays $1 and then tosses a fair coin until either a head occurs or he has tossed the coin four times. He receives 50 cents for each toss. Determine the expected winnings for one trial of the game.

Solution

Ans: In a single trial of the game, the course of action can be as below:

a) H1, (T1 and H2), (T1, T2, H3) , (T1,T2,T3,H4) OR (T1,T2,T3,T4)

He receives $0.5 for each toss.

The expected winnings can be found as(0.5*0.5) + 0.5(0.5*0.5)*2 +0.5(0.5*0.5*0.5)*3 +0.5(0.5^4)*4 + 0.5(0.5^4)*4 = 0.25 + 2.5+0.125+0.125=$ 3