Question

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 1

The formula for the expected value is:

`E(X)=\sum x_iP(x_i),`

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:

`(3)/(6)=(1)/(2).`

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

Therefore:

`E(X)=496((1)/(2))+1020((1)/(2))=758.`

Answer: $758.