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# Expected value of coin toss?

So say after a player pays R200 to play a game, five fair coins are tossed. If four or more heads are obtained, the player wins the game, otherwise they lose their entire bet.

Please help on how you would calculate the fair pay out?

### 2 Answers

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- Anonymous2 years ago
P(H = 4) + P(H = 5) = C(5,4)*((1/2)^5) + C(5,5)*((1/2)^5) = 3/16 = 0.1875 = 18.75%;

To be a fair payout if the probability does happen for every one dollar you bet you should get

16/3 dollars back, therefore a fair pay out will be

200*(16/3) = 3200/3 which is about 1066.67

- Steve ALv 72 years ago
P(4H) = 5C4*(1/2)^5 = 5/32

P(5H) = 5C5*(1/2)^5 = 1/32

P(4+) = 6/32 = 3/16

(3/16)x = 200

x = 3200/3 = 1066 2/3

Payout = R1066 2/3. This includes the return of the original R200.

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