You start your shift as a cashier with your drawer containing ten $1 bills, 5 $2 bills, three $5 bills, one $10 bill and one $100 bill. Find the expectation if one bill is selected.
To find the expectation if one bill is selected, we need to calculate the probability of selecting each type of bill and multiply it by the value of that bill, and then sum up the results.
First, let's find the probability of selecting each type of bill:
- There are a total of 10 + 5 + 3 + 1 + 1 = 20 bills in the drawer.
- The probability of selecting a $1 bill is 10 / 20 = 0.5 (or 50%).
- The probability of selecting a $2 bill is 5 / 20 = 0.25 (or 25%).
- The probability of selecting a $5 bill is 3 / 20 = 0.15 (or 15%).
- The probability of selecting a $10 bill is 1 / 20 = 0.05 (or 5%).
- The probability of selecting a $100 bill is 1 / 20 = 0.05 (or 5%).
Now, let's calculate the expectation:
- The expectation is the weighted average of the values of all possible outcomes.
- For each bill, we multiply its value by its probability and sum up the results.
Expectation = ($1 * 0.5) + ($2 * 0.25) + ($5 * 0.15) + ($10 * 0.05) + ($100 * 0.05)
= $0.5 + $0.5 + $0.75 + $0.50 + $5.00
= $7.25
Therefore, the expectation if one bill is selected from the drawer is $7.25.
10.23
(1*1 + 5*2 + 3*5 + 1*10 + 1*100)
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(1+5+3+1+1)