A person randomly selects one of six envelopes. Each envelope contains a check that the person gets to keep. Determine the person's expectation if the six envelopes contain checks for $\$ 130, \$ 215, \$ 259, \$ 436, \$ 456$, and \$1011

Step 1 ：A person randomly selects one of six envelopes. Each envelope contains a check that the person gets to keep. The six envelopes contain checks for \$130, \$215, \$259, \$436, \$456, and \$1011.

Step 2 ：The expectation of a random variable is the long-term average or mean value of the random variable. It is calculated by multiplying each possible outcome by their probability and then summing all these values.

Step 3 ：In this case, the person has an equal chance of selecting any of the six envelopes, so the probability of each outcome is \(\frac{1}{6}\).

Step 4 ：The expectation is therefore the sum of each check amount multiplied by \(\frac{1}{6}\).

Step 5 ：Final Answer: The person's expectation when selecting one of the six envelopes is \(\boxed{\$417.83}\).