Probability question

Question

A cash register contains 5 one-dollar bills, 6 five-dollar bills, and 4 ten-dollar bills. You take 3 random bills without replacement. What is the list of possible outcomes for the total sum of money drawn? Draw the decision tree and calculate probabilities for the different total sums that can be drawn.

Answer 1

Hi

I drew a tree of all the possible outcomes of the three draws Next to each combination I have included the probabilities. For example to calculate the probability of drawing three $1 bills. First we recognize that there are 5 $1 bills out of 15 total bills (5/15). Then we multiply that the probability of drawing another $1 bill given that we drew a $1 bill on the first draw. There are now 4 $1 bills out of 14 bills total. (5/15)*(4/14). We then multilply that by the probability of drawing another $1 bill out of the remaining 13 bills (3/13). You do that for each of the sets of branches. Next count up the sum of the bills selected. Group the same sums together and add up the related probabilities to answer the question. For example you can see that there is only one way to draw a sum of $3. Its probability is 0.022. The first row of the last three columns show outcome $3, frequency 1, probability 0.022. The next row shows that there are three sets of branches that end up with a sum of 7. Add the probabilities together of the branches that sum to 7. It equals 0.132.

Let me know if you have further questions. :)

Dian