< ALGEBRA 1>
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Answer:
The expected value of the safe bet equal $0
Step-by-step explanation:
If
is a finite numeric sample space and
for k=1, 2,..., n
is its probability distribution, then the expected value of the distribution is defined as
What is the expected value of the safe bet?
In the safe bet we have only two possible outcomes: head or tail. Woodrow wins $100 with head and “wins” $-100 with tail So the sample space of incomes in one bet is
S = {100,-100}
Since the coin is supposed to be fair,
P(X=100)=0.5
P(X=-100)=0.5
and the expected value is
E(X) = 100*0.5 - 100*0.5 = 0