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Sagot :
To find the E(X) expected value, you come up with the different probabilities for each outcome
your set of outcomes after 3 tosses would be = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} where H is heads and T is tails
Each element has a probability of 1/8 so let x represent number of tails
Probability (x) = P (x)
P (0) = 1/8
P (1) = 3/8
P (2) = 3/8
P (3) = 1/8
The E(x)=Summation (x times P(x))
E ( X ) = (0) (0.125) + (1) (0.375) + (2) (0.375) + 3 (0.125) = 1.5
Now which probability is 1.5 tails? None, so it is either 2 tails or 1 tails
So you can expect to lose money in 1 game
But as you play more games the probability of getting 3 tails becomes more and more likely, so you can expect to win in a 100 games
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