Describe the likelihood that matches the following probabilities:
A probability of 0.2.
A probability of 0.9.
A probability of 0.5.
A probability of 0.
A probability of \dfrac{1}{10}.
A probability of 1.
State the likelihood of the occurrence of the following:
Scoring 140\% on an exam.
Getting a number greater than two when rolling a die.
Estimate the probability of the following events to one decimal place:
You will flip tails in a coin toss.
It will rain somewhere in Australia tomorrow.
You will score 110\% on the next maths test.
You'll fly a rocket to school.
A standard six-sided die is rolled. Find the probability of the following events:
Rolling a prime number.
Rolling an even number.
Rolling a number less than 3.
Every 60 seconds, a traffic light remains green for 21 seconds, yellow for 3 seconds and red for 36 seconds. Find the probability of the following events:
Arriving at the traffic light when it is green.
Arriving at the traffic light when it is yellow.
Arriving at the traffic light when it is red.
The box shown contains 3 yellow balls, 4 red balls, 1 white ball, and 2 striped balls:
Iain selects one ball without looking.
Find the probability that Iain selects:
A red ball.
A white ball.
A yellow ball.
A striped ball.
Which type of ball is Iain most likely to select?
A card is drawn at random from a standard deck. Find the probability that the card is:
A diamond.
A spade.
A five.
A nine.
A black card.
A face card.
A red nine.
A black nine.
A king of diamonds.
An odd-numbered black card.
The following spinner has 8 equal sectors. 3 sectors are purple, 2 sectors are red, 2 sectors are yellow, and 1 sector is blue:
When the spinner is spun, find the probability that:
It lands on purple.
It does not land on purple.
Find the the sum of the probabilities from part (a). Explain the reason behind this sum.
The following dice is rolled.
Find the probability of:
Rolling a four.
Not rolling a four.
Find the the sum of the probabilities from part (a). Explain the reason behind this sum.
Find the probability that the complement of the following events will occur:
An event that has a probability of \dfrac{4}{5}.
An event that has a probability of 0.64.
A jar contains a number of marbles, where some of the marbles are blue and the rest are red.
If the probability of picking a red marble is \dfrac{9}{10}, find the probability of picking a blue marble.
A biased coin is flipped, with heads and tails as possible outcomes. Find P(\text{heads}) if P(\text{tails}) = 0.56.
A bag contains 34 red marbles and 35 blue marbles. If picking a marble at random, find:
P(\text{Red})
P(\text{Not Red})
P(\text{Not Blue})
The 26 letters of the alphabet are written on pieces of paper and placed in a bag. If one letter is picked out of the bag at random, find the probability of the following:
Not selecting a B.
Not selecting a K, R or T.
Not selecting a T, L, Q, A, K or Z.
Selecting a letter that is not in the word PROBABILITY.
Selecting a letter that is not in the word WORKBOOK.
A card is drawn at random from a standard deck. Find the probability that the card is:
Not a heart.
Not a two.
Not a black card.
Not a red three.
Not a queen of clubs.
At a particular school, there are 270 students in Year 9 and 180 students in Year 10. 20\% of the Year 9 students and 45\% of the Year 10 students like Geography.
Find the probability that a randomly chosen Year 9 student does not like Geography.
Find the probability that a randomly chosen student is in Year 9 and does not like Geography.
Find the probability that a randomly chosen student from either year group does not like Geography.
Two events A and B are mutually exclusive.
If P(A) = 0.37 and P(A\text{ } \text{or}\text{ } B) = 0.73, find P(B).
If P(A) = 0.8, P(B) = 0.75 and P(A\text{ } \text{and} \text{ } B)= 0.6, find P(A\text{ } \text{or}\text{ } B).
A card is drawn at random from a standard deck. Find the probability that the card is:
A king or a 3.
A spade or a diamond.
An ace of spades or an ace of clubs.
A ten, jack, queen, king or an ace.
An ace of spades or a king of hearts.
A red or a diamond.
An ace or a diamond.
A black or a face card.
Not a red ten or black jack.
A bag contains 86 marbles, some of which are black and some of which are white. If the probability of selecting a black marble is \dfrac{33}{43}, find:
The number of black marbles in the bag.
The number of white marbles in the bag.
Consider the following formula: n\left(A \cup B\right) = n\left(A\right) + n\left(B\right) - n\left(A \cap B\right).
Translate the formula in words.
Does the formula hold for the sets A and B shown in the Venn diagram?
Does the formula hold for the sets \\A = \left\{2, 4, 5, 6, 8, 9\right\} and \\B = \left\{0, 1, 3, 4, 5, 7, 10\right\}?
Use the Venn diagram to explain why we must subtract n\left(A \cap B\right).
A standard six-sided dice is rolled. Find the probability of rolling:
The number 4.
An odd number.
A 4 or an odd number.
An even or prime number.
A number that is even and prime.
An even number or a factor of 6.
A factor of 9 or an even number.
A number less than 3.
A number greater than 5.
A number less than 3 or greater than 5.
For each of the following probability Venn diagrams:
Calculate the value of x in the diagram.
State whether A and B are mutually exclusive.
The following spinner is spun and a normal six-sided die is rolled at the same time. The product of their respective results is recorded.
Construct a table to represent all possible outcomes.
State the total number of possible outcomes.
Find the probability of an odd product.
Find the probability of rolling a 5 on the dice and scoring an even product.
Find the probability of spinning a 3 on the spinner or scoring a product which is a multiple of 4.
The following two spinners are spun and the sum of their results are recorded:
Construct a table to represent all possible outcomes.
State the total number of possible outcomes.
Find the probability that the first spinner lands on an even number and the sum is even.
Find the probability that the first spinner lands on a prime number and the sum is odd.
Find the probability that the sum is a multiple of 4.
The following spinner is spun and a normal six-sided die is rolled. The result of each is recorded:
| W | X | Y | Z | |
|---|---|---|---|---|
| 1 | 1,W | |||
| 2 | 2,Z | |||
| 3 | ||||
| 4 | ||||
| 5 | 5,X | |||
| 6 |
Complete the table above to represent all possible combinations.
State the total number of possible outcomes.
Find the probability that the spinner lands on X and the dice rolls a prime number.
Find the probability that the spinner lands on W and the dice rolls a factor of 6.
Find the probability that the spinner doesn’t land on Z or the dice doesn't roll a multiple of 3.
The following two spinners are spun and the result of each spin is recorded:
Complete the given table to represent all possible combinations:
State the total number of possible outcomes.
Find the probability that the spinner lands on a consonant and an even number.
| Spinner | A | B | C |
|---|---|---|---|
| 1 | 1,A | ||
| 2 | 2,C | ||
| 3 |
Find the probability that the spinner lands on a vowel or a prime number.
A three-digit number is to be formed from the digits 4, 5 and 9, where the digits cannot be repeated.
List all the possible numbers in the sample space.
Find the probability that the number formed is:
Odd
Even
Less than 900.
Divisible by 5.
Two dice are rolled, and the combination of numbers rolled on the dice is recorded.
Construct a table to represent the possible combinations.
Find the following probabilities for the two numbers rolled:
P(1 and 4)
P(1 then 4)
P(difference =4)
P(product =12)
P(difference \leq 2)
P(difference =3)
P(product =20)
P(difference\, \leq 1)
The numbers appearing on the uppermost faces are added. State whether the following are true.
A sum greater than 7 and a sum less than 7 are equally likely.
A sum greater than 7 is more likely than a sum less than 7.
A sum of 5 or 9 is more likely than a sum of 4 or 10.
An even sum is more likely than an odd sum.
Consider the following four numbered cards:
Two of the cards are randomly chosen and the sum of their numbers is listed in the following sample space:
\left\{15, 10, 8, 11, 9, 4\right\}
Find the missing number on the fourth card.
If two cards are chosen at random, find the probability that the sum of their numbers is:
Even
At least 10
The results from a recent survey showed that 79 people speak Spanish or French. Of these, 49 speak Spanish, and 18 speak both Spanish and French.
Find the number of people surveyed who speak French.
The result of a recent survey showed that 34 people own a dog, 33 own a cat, and 13 own both a dog and a cat.
How many people surveyed own at least one dog or cat?
The number of movie, concert and music tickets on offer as a prize are in the ratio 8:19:3.
Find the probability that the winner will be given a concert ticket.
The winner doesn’t want to see a musical. Find the probability that they get a ticket they do want.
A circular spinner is divided into unequal parts. The green sector takes up an angle of 250 degrees at the centre. The red sector takes up an angle of 60 degrees at the centre and the blue sector takes up the remainder of the spinner.
Find the probability that the spinner will land on blue.
While discussing dominant physical traits, some students completed a survey of their eye colour. Each student nominated one colour, and the results are shown in the table:
What percentage of students had hazel eyes?
Find the least number of students that could have completed the survey.
| Brown | Blue | Green | Hazel |
|---|---|---|---|
| 70\% | 15\% | 2\% |
The Venn diagram shows the decisions of 448 workers choosing to work and workers choosing to strike on a particular day of industrial action.
Find the probability that a worker selected randomly chose to:
Strike
Strike and work
Work and not strike
Work or strike
Among a group of 63 students, 12 students are studying philosophy, 48 students are studying science, and 7 students are studying neither subject.
How many students are studying philosophy and science?
If a student is picked at random, find the probability that they study at least one of these subjects.
Find the probability that a randomly selected student studies only one of the subjects.
A grade of 172 students are to choose to study either Mandarin or Spanish (or both). 79 students choose Mandarin and 111 students choose Spanish.
How many students have chosen both languages?
If a student is picked at random, find the probability that the student has chosen Spanish only.
If a student is picked at random, find the probability that the student has not chosen Mandarin.