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A person randomly selects one of six envelopes. Each envelope contains a check that the person getsto keep. Determine the person's expectation if three envelopes contain a $496 check and three envelopes contain a $1020 check.SaveThe expected value is $

Answer :

The formula for the expected value is:

[tex]E(X)=\sum x_iP(x_i),[/tex]

where x_i are the possible values and P(x_i) the probabilities.

We are given that 3 envelops contain a $496 check, therefore, the probability of choosing a $496 check is:

[tex]\frac{3}{6}=\frac{1}{2}.[/tex]

Analogously, we get that the probability of choosing a $1020 check is 1/2.

Therefore:

[tex]E(X)=496(\frac{1}{2})+1020(\frac{1}{2})=758.[/tex]

Answer: $758.