## Tree Diagrams Exercise

1. . Three fair coins are tossed. One side is called "heads" and the other side is called "tails". Draw a tree diagram to show all of the possible combinations and use the diagram to find the probability that:

a. All three coins are heads
b. There are two heads and a tail (in any order)
c. There is at least one head.
d. Given that the first coin is a head, the other two coins are tails.

 2. A company buys three brands of laptop computers: Brand A (50%) , Brand B (15%) and Brand C(35%). Brand A have a 30% probability of developing a fault in the first year, Brand B 15% and Brand C 10%. Draw a tree diagram to show this situation and find the probability that a computer will develop a fault in its first year. 3. A bag contains 20 coloured marbles, 8 blue and 12 red. A marble is taken from the bag, its colour noted and then replaced in the bag. This is repeated twice.

Draw a tree diagram to help calculate the probability that only two of the marbles chosen are blue.

4. The same bag, as in question 3, contains 20 coloured marbles, 8 blue and 12 red. A marble is taken from the bag, its colour noted and it is NOT replaced.

This is repeated twice. Draw a tree diagram to help calculate the probability that only two of the marbles chosen are blue.

5. Shonag's pencil case contains three blue pens, two red pens and one green pen.
If she takes out two pens:

a. Draw a probability tree to show this situation.

Use the probability tree to find the probability that:

b. The first one will be blue and the second one will be red.
c. No blue pens will be drawn

d. Exactly one pen will be red.
e. At least one pen will be red.

6. One of the games that may operate in the casino is played as follows:

\$1 is paid to enter the game. A fair six-sided die is rolled.

If an even number turns up, the player loses; otherwise the die is rolled a second time. On the second roll, if a "1" turns up, the player wins \$3; otherwise, the player loses.

If the player has won on the second roll, the die is rolled a third time; if a "2" turns up, the player wins another \$5; otherwise, the game ends.

Note: The game ends when the player loses, or after the third roll of the die.

Draw a probability tree showing the possible outcomes of the game. Clearly label the branches of the tree, and show the relevant probabilities.

a. What is the probability that a player wins \$8?

b. What is the probabiity that a player wins \$3?

c. What is the probabiity that a player loses on the 2nd throw?