Q; The door prizes at a dance are gift certificates from local merchants.

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.

I'm confused as to how the tree diagram for this scenario, please explain the and show how it is done.

Answer 1

Let the prizes be x, y and z.

There are 12 total prizes

The possibility of picking x first is 4/12

The possibility of picking y first is 5/12

The possibility of picking z first is 3/12

From a starting node, take three branches, one for each prize. Then from each of those nodes, take three branches one, for each prize, x,y,z.

The possible branches for picking the first two prizes are:

xx

xy

xz

yx

yy

yz

zx

zy

zz

Now you need to label each branch with it's probability. For example

xx = 4/12 and 3/11

xy = 4/12 and 5/11

xz = 4/12 and 3/11

yx = 5/12 and 4/11

and so on

To compute the probabilities of non-matching picks, you have to add the probabilities.

For example P(xy) + P(yx)