12.5 Homework: Tree Diagram

Name:______Block:______Date:______12.5 Homework: Tree Diagram

1. If two dates are selected at random from the 365 days of the year, use the counting principle to determine the number of possible outcomes if the dates are selected a. With replacement

b. Without replacement

2. Your television remote control has buttons for digits 0-9. If you press two buttons, how many numbers are possible if a. The same button may be pressed twice.

b. The same button may not be pressed twice.

Use the counting principle to determine the answer to part (a). Assume that each event is equally likely to occur. 3. A couple plans to have two children. a. Determine the number of points in the sample space of the possible arrangements of boys and girls.

b. Construct a tree diagram and list the sample space.

Find the probability that the couple has c. Two girls.

d. At least one girl.

e. A girl and then a boy.

4. A box contains three cards. On one card there is a circle. On another card there is a square and on the third card there is a triangle. Two cards are selected at random without replacement. a. Determine the number of points in the sample space.

b. Construct a tree diagram and determine the sample space. Find the probability that c. Two circles are selected.

d. A square and then a triangle are selected.

e. At least one circle is selected.

5. A couple plans to have three children. a. Determine the number of points in the sample space of possible arrangements of boys and girls.

Find the probability that c. No boys.

d. At least one girl.

e. Either exactly two boys or two girls.

f. Two boys first, then one girl.

6. At a homeowners association meeting, a board member can vote yes, no, or abstain on a motion. There are three motions the board is voting on. a. Determine the number of points in the sample space.

Find the probability that a board member votes c. No, yes, no in that order.

d. Yes on exactly two of the motions. e. Yes on at least one motion.

7. Susan Foreman has to purchase a box of cereal, a bottle of soda, and a can of vegetables. The types of cereal, soda, and vegetables she is considering are shown below.

Cereal: Rice Krispies, Frosted Flakes, Honeycombs Soda: orange, black cherry, ginger ale Vegetables: peas, carrots

a. Determine the number of points in the sample space.

b. Construct a tree diagram and determine the sample space.

Find the probability that she selects c. Honeycomb for the cereal.

d. Rice Krispies and ginger ale.

e. A soda other than black cherry.