Problem

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 three envelopes contain a $539 check and three envelopes contain a $1000 check

Answer

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Answer

The person's expectation is $769.5. So, the final answer is 769.5.

Steps

Step 1 ：Define the total number of envelopes as 6.

Step 2 ：Define the number of envelopes containing a $539 check as 3.

Step 3 ：Define the number of envelopes containing a $1000 check as 3.

Step 4 ：Calculate the probability of selecting an envelope with a $539 check as 36=0.5.

Step 5 ：Calculate the probability of selecting an envelope with a $1000 check as 36=0.5.

Step 6 ：Calculate the expectation as 0.5×539+0.5×1000=769.5.

Step 7 ：The person's expectation is $769.5. So, the final answer is 769.5.

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