9.02 Theoretical probability
The following spinner is spun once:
What are the possible outcomes?
What outcome is the most likely?
A standard six-sided die is rolled. State the likelihood that the outcome is:
A 2 or greater?
A 7 or greater?
A twelve-sided die is rolled. State the likelihood that the outcome is 8 or greater?
One marble is drawn out of the following jar containing 3 black, 3 red, and 6 blue marbles:
State the color of the marble that you are most likely to draw.
State the likelihood that you draw a marble that is not blue.
The three cards below are shuffled. One card is then drawn at random:
State the likelihood of drawing a Heart.
State the likelihood of drawing a number card.
The four cards below are shuffled. One card is then drawn at random:
State the likelihood of drawing a Jack, Queen or King.
State the likelihood of drawing a card with a number less than 4.
Consider the spinner shown:
What is the most likely symbol to spin?
State the likelihood of spinning a ball.
Which one of the following pairs of events have an equal chance?
Spinning an apple or a pig.
Spinning a star or a ball.
Spinning a pig or a star.
Spinning a ball or a pig.
Consider the spinner shown:
State whether the following events have an equal chance:
Spinning an even number.
Spinning 7 or more.
Spinning 12 or less.
Spinning 7 or less.
State the likelihood of spinning 15 or more.
What event is most likely to happen?
State the likelihood that corresponds to each of the following probability values using one of the following terms: Impossible, Unlikely, Likely or Certain.
\dfrac{4}{5}
0.1
1
0
0.6
\dfrac{9}{10}
\dfrac{2}{10}
10\%
70\%
\dfrac{1}{8}
Vincent rolls a twelve-sided die and writes down whether he rolls 6 or more. If he does, he writes "yes", otherwise he writes "no".
List all possible outcomes that correspond to the event where he writes "yes".
Kenneth has a six-sided die. Lisa has a twelve-sided die. They decide to roll both their dice and the winner is the person who rolls the greatest number. Who is more likely to win?
Estimate the probability of the following events as a decimal number:
It will rain somewhere in Australia sometime this month.
You meet someone today and correctly guess their birthday.
Which of these events has a probability closer to 0.25?
You roll a six-sided die and get a 5 or more.
You find \$100 on the ground today.
Which of these events has a probability closer to 0.75?
You flip a coin ten times and get at least one tails.
You roll a twelve-sided die and get 3 or more.
Given an event with a probability of 4\%, determine whether the following statements are true or false:
It is likely to occur.
It is unlikely to occur.
It should occur 4 times every 100 trials.
It should occur 2 times every 100 trials.
It should occur 20 times every 500 trials.
It should never occur.
A twelve-sided die is rolled.
Find the probability of rolling 5 or more.
Find the probability of rolling less than 5.
For each of the following spinners, find the probability of getting a star. Write your answer as a percentage.
A jar contains 10 marbles in total. Some of the marbles are blue and the rest are red.
If the probability of picking a red marble is \dfrac{4}{10}, how many red marbles are there in the jar?
Find the probability of picking a blue marble.
Paul has 23 marbles in a bag and 4 of them are black. Paul picks a marble from the bag without looking. Find the probability that Paul picks a black marble.
Consider the following spinner:
Find the probability of spinning:
A pig.
A ball or a pig.
A pig or an apple.
An apple or a star.
Consider the following spinner:
Find the probability of getting the following shapes:
An apple.
A pig.
An elephant.
A ball.
A pig or a ball.
Anything but an apple.
An elephant, a star or a teddy bear.
Anything but a ball or teddy bear.
Determine whether the following events have a probability less than 10\%.
Spinning a teddy bear.
Spinning a star.
Spinning an apple.
Spinning a ball or an elephant.
A single marble is drawn from the following jar 5 red, 7 blue and 8 black marbles:
Find the probability of drawing a blue marble. Write your answer as a percentage.
Find the probability of drawing a blue marble or a red marble. Write your answer as a percentage.
A card is drawn from a standard deck of cards:
Find the probability of drawing the Jack of Hearts or the Jack of Clubs.
Rosey draws a 6 of Spades and puts it back in the deck and asks you to draw a card. Find the probability that you will draw a card with a number larger than 6, and the same color as Rosey's card.
Yuri has 5 blue marbles, 1 red marble, 1 yellow marble and 1 black marble in a bag. Yuri picks a marble from the bag without looking. Find the probability that Yuri picks a blue marble.
A bag contains 21 red marbles and 26 blue marbles. Find the probability of drawing a red marble.
A spinner has ten sectors of the same size:
5 of the sectors show a star.
2 of the sectors show an apple.
3 of the sectors show an elephant.
Find the probability of spinning an elephant.
A letter is chosen at random from the word COCOONS.
Which letter is most likely to be chosen?
Find the probability that the chosen letter is a "C".
A bag contains 49 marbles. 24 of them are red and the rest are of them are blue.
Find the probability of drawing a blue marble.
The numbers from 2 to 10 are written on separate cards. One card is chosen at random. Find the probability that the number is:
A multiple of 2.
A prime number.
A number less than 6.
A two-digit number is formed only using the digits 3 and/or 2.
Find the probability that the number formed is odd.
Find the probability that the number formed is more than 30.
Emma rolls two four-sided dice and multiplies the two numbers she rolls together.
Find the probability that the number formed is even.
Find the probability that the number formed is larger than 6.
A full set of scrabble tiles is shown in the diagram below. The last two letters are the two "blank" tiles:
| A | A | A | A | A | A | A | A | A | B |
| B | C | C | D | D | D | D | E | E | E |
| E | E | E | E | E | E | E | E | E | F |
| F | G | G | G | H | H | I | I | I | I |
| I | I | I | I | I | J | K | L | L | L |
| L | M | M | N | N | N | N | N | N | O |
| O | O | O | O | O | O | O | P | P | Q |
| R | R | R | R | R | R | S | S | S | S |
| T | T | T | T | T | T | U | U | U | U |
| V | V | W | W | X | Y | Y | Z |
One letter tile is drawn at random:
Find the probability that it is a "G" or an "R".
Find the probability of drawing a vowel.
Luigi and Danielle enter a raffle where 80 tickets are on sale. Luigi buys 1 ticket and Danielle buys 5 tickets.
Find the probability that Luigi wins if all the tickets were sold.
Find the probability that Danielle wins if all the tickets were sold.
Find the probability that Danielle wins if only 70 tickets were sold.
A three-digit number is formed only using the digits 2, 7, and/or 8. Some of the possible three-digit numbers are listed below:
222, \quad 227, \quad 228, \quad 272, \quad 277, \quad 278, \quad 282, \quad 287, \quad 288, \\ 722, \quad 727, \quad 728, \quad 772, \quad 777, \quad 778, \quad 782, \quad 787, \quad 788Find the probability that the number formed is odd.
Find the probability that the number formed is palandromic (the same forwards as backwards).
Neil takes the following cards and shuffles them up. He draws one card, shows it to you, and keeps it. You then draw one card from the remaining seven cards, and you win if the number on your card is greater than Neil's.
Find your chance of winning if Neil draws the following cards:
