Question

assume a person pays $1 to play the following game. Four coins are tossed. If all coins show the same (all heads or all tails), the player wins $6; otherwise, the player loses. Find the expected value for this game.

Answer 1

I believe that answer shall be 24

Answer 2

For each toss the probability is 0.5 head and 0.5 tail.
As you have 4 coins you have 0.5 probability for head in each coin also about the tails.
The probability of all heads is 0.5^4 and all tails is 0.5^4 so the probability of win is 0.5^4+0.5^4=0.125
The expected value is $6*0.125 - $1*(1-0.125)= -0.125$

(1-0.125) is the propability of fail.
-$1 is the money that you would lose