Question

I have 5 identical envelopes. You get to pick one.

1 envelope has $10 in it.
2 envelopes have $1 in them and 2 envelopes have a quarter (25 cents) in them.

What is the expected value?

Answer 1

The expected value is $2.50.

Step-by-step explanation:

The expected value can be calculated by multiplying the value of each outcome by its corresponding probability and summing the results.

In this case:

• 1 envelope has $10 with a probability of 1/5
• 2 envelopes have $1 with a probability of 2/5
• 2 envelopes have a quarter with a probability of 2/5

So the expected value can be calculated as:

Expected value = (1/5) * $10 + (2/5) * $1 + (2/5) * $0.25

Simplifying the equation:

Expected value = $2 + $0.4 + $0.1

Therefore, the expected value is $2.50.