Please help with question I really don't understand!

Question

1. The door prizes at a dance are gift certificates from local merchants. there are four $10 certificates, five $20 certificates, and three $50 certificates. The prize envelopes are mixed together in a bag and are drawn at random.

a) Use a tree diagram to illustrate the possible outcomes for selecting the first two prizes to be given out.

Please show all steps for this question and a explanation because I really don't understand why the tree diagram looks like that from the answer.

Answer 1

Lia, On Left side of paper in middle of page draw a dot and three lines with arrows. top line going angle up middle line straight and bottom line anglingi down. Maybe two inches length each for the lines.

top line is labelled $10. and probability 4/12, mdidlle line $20 and probability 5/15, bottome line $50 and probability 3/12. That represents prize one being chosen.

Now on the top line where arrow is, draw thre lines one angling up (label that line $10 and probability 3/11), one straight (label that one $20 and probability 5/11) anf one angling down (label that one $50 and probability 3/11).

on the original middle line where arrow is draw three lines, $10 probability 4/11, $20. probability 4/11,

and $50 probability 3/11.

on original bottom line draw three lines from where the arrow is. $10 probability 4/11, $20. probability 5/11, and $50 probability 2/11.

The second set of lines indicate the proibability of the outcome based on the previous outcome.

To go a bit further ---what is probability the first two prize are $10 and $10, answer = (4/12)*(3/11). What is probability of first two prizes being $10 and $20, answer=(4/12)*(5/11). What is probability of first two prizes being $10 and $50, answer=(4/12)*(3/11). What is probabiliry of first two prizes being $20 and $10, answer=(5/12)*4/11) and you can continue down the other outcomes and multiply the probabilities together.

Answer 2

$10

$10 $20

$50

$10

$20 $20

$50

$10

$50 $20

$50