Question

a jar contains 25 $1 bills 5 $5 bills 5 $10 bills 3 $20 bills 4 $50 bills 2 $100 bill every day for one year (365 times) you get to randomly pick a bill from the jar (the jar is refilled after every pick) for the year, what is the expected value of the total money you have won?

Answer 1

Expected value in probability is used to calculate the average amount of money one can expect to win when drawing bills from a jar daily for a year. We calculate the expected value per draw by multiplying each bill's value by its probability and summing those products. Then multiply by 365 to get the expected total value for the year.

Step-by-step explanation:

The subject of this question is expected value, which is a fundamental concept in probability and statistics. The problem presented is a real-world application of expected value, where we calculate the average amount of money one could expect to win after repeatedly drawing bills from a jar over a year.

First, we find the expected value per draw by calculating the weighted average of all possible outcomes. For each denomination, this involves multiplying the value of the bill by the probability of drawing that bill. We sum up these products for all bill denominations to get the expected value per single draw. Since the jar is refilled after each pick, each draw is independent, and the probabilities remain constant throughout the year.

Here's how we calculate it step by step:

1. Calculate the total number of bills in the jar.
   
   
2. For each bill type, calculate the probability of drawing that bill. This is the number of specific bills divided by the total number of bills.
   
   
3. Multiply the value of each bill by its probability to find the expected value for each bill type.
   
   
4. Add up all these expected values to find the expected value per draw.
   
   
5. Multiply the expected value per draw by 365 to find the expected total value for the year.