You are offered the following gamble: Flip two fair coins. If at least one head comes up, you win $12. If not, you lose $24. What is the expected value of this gamble?

$3

Step-by-step explanation:

Flipping two fair coins :

Sample space :

{TH, HT, TT, HH}

Atleast one head = 12

If not = - 24

Probability of atleast one head = 3/4

If not ; probability of 2 tails = 1/4

Hence,

X 12 -24

P(x) ___0.75 0.25

Expected value for of gamble E(x) :

Σx * p(x) = (12 * 0.75) + (-24 * 0.25)

E(x) = 9 - 6

E(x) = 3

Expected value of gamble = $3

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