Secondary II 7.1-7.3

Tree Diagram

100

A jar has 4 red marbles and 4 blue marbles.  Three marbles are drawn and removed from the jar.  Draw a tree diagram for the situation.

200

A coin is flipped four times.  Draw a tree diagram for the possible outcomes.

300

A person has four keys, one of which will unlock a door.  Draw a tree diagram to show the possible outcomes.

400

In the game of Monopoly, if you are in Jail you can only get out if you roll a double.  If you do not roll a double after three times, you pay $50 to get out of Jail.  Draw a tree diagram for the possible outcomes.  

Counting Principle

100

You take a survey with five “yes” or “no” answers. How many different ways could you complete the survey?

32

200

In a certain country telephone numbers have 9 digits. The first two digits are the area code (03) and are the same within a given area. The last 7 digits are the local number and cannot begin with 0. How many different telephone numbers are possible within a given area code in this country?

300

A fast-food restaurant has a meal special: $5 for a drink, sandwich, side item and dessert. The choices are:

• Sandwich: Grilled chicken, All Beef Patty, Vegeburger and Fish Filet.
• Side: Regular fries, Cheese Fries, Potato Wedges.
• Dessert: Chocolate Chip Cookie or Apple Pie.
• Drink: Fanta, Dr. Pepper, Coke, Diet Coke and Sprite.

120

400

When a button is pressed, a computer

program outputs a random even number

greater than 0 and less than 12.  You press

the button six times.

Permutation/ Combination (Easy)

100

₆P₃

120

200

₁₀C₄

210

300

₁₅P₃ + ₈P₅

9450

400

₆C₀ * ₇C₇ * (₄C₂ - ₅C₁)

1

Permutation/ Combination (Harder)

100

You just got a free ticket for a boat ride, and you can bring along 222 friends! Unfortunately, you have 555 friends who want to come along.

200

How many 3 digit numbers can we make using the digits 2, 3, 4, 5, and 6 without repetitions?

300

How many unique ways are there to arrange the letters in the word PRETTY?

360

400

A committee including 3 boys and 4 girls is to be formed from a group of 10 boys and 12 girls. How many different committee can be formed from the group?

Probability

100

A jar contains 3 red marbles, 7 green marbles and 10 white marbles. If a marble is drawn from the jar at random, what is the probability that this marble is white?

200

Three coins are tossed up in the air, one at a time. What is the probability that two of them will land heads up and one will land tails up?

300

An MP3 player is set to play songs at random from the fifteen songs it contains in memory. Any song can be played at any time, even if it is repeated. There are 5 songs by Band A, 3 songs by Band B, 2 by Band C, and 5 by Band D. If the player has just played two songs in a row by Band D, what is the probability that the next song will also be by Band D?

400

Two dice are rolled, find the probability that the sum is equal to 5.