Hadyn is looking for a way to randomly choose a prime number between 1 and 20.
He first flips a coin to decide 0 or 1 and depending on the result he then rolls one of two four-sided dice, shown in the tree diagram. He arrives at his number by putting the coin number in front of the dice number.
List the sample space of numbers created.
Find the probability that the number will be 17.
Find the probability that the number will be less than 10.
Find the probability that the number will end in a 3.
An ice-cream shop randomly picks one of six flavours of ice-cream to sell at a discounted price each day. Three of the flavours are sorbet and the other three are gelato.
The three sorbet flavours are raspberry \left(R\right), lemon \left(L\right) and chocolate \left(C\right). The three gelato flavours are vanilla \left(V\right), mint \left(M\right) and chocolate \left(C\right).
List the sample space for which ice-cream type and flavour may be chosen.
Find the probability that the lemon sorbet is selected.
Find the probability that the flavour will be chocolate.
Three cards labelled 2, 3, 4 are placed face down on a table. Two of the cards are selected randomly to form a two-digit number. The possible outcomes are displayed in the following probability tree:
List the sample space of two digit numbers produced by this process.
Find the probability that 2 is a digit in the number.
Find the probability that the sum of the two selected cards is even.
Find the probability of forming a number greater than 40.
Consider the tree diagram showing all the possible outcomes when a die is rolled twice:
State the total number of outcomes.
Find the probability of:
Rolling a 1 and a 1.
Rolling a 3 and a 5.
The first die rolling a 5.
The second die rolling a 5.
Rolling a double 5.
Rolling the same number twice.
Rolling two different numbers.
Rolling two odd numbers.
Rolling two even numbers.
Rolling two numbers less than 3.
Rolling two numbers more than 4.
Rolling a 4 and a 7.
Consider the tree diagram for an experiment where three fair coins are tossed:
State the total number of outcomes.
List the outcomes.
Find the probability of obtaining:
Three tails.
TTH in this order.
THH in this order.
Two tails and a head.
A coin is tossed twice.
Construct a tree diagram showing the results of the given experiment.
Use the tree diagram to find the probability of getting:
Exactly 1 head.
2 heads.
No heads.
1 head and 1 tail.
Construct a tree diagram showing all the ways a captain and a vice-captain can be selected from Matt, Rebecca and Helen.
Construct a tree diagram showing the following:
All possible outcomes of boys and girls that a couple with three children can possibly have.
All the ways the names of three candidates; Alvin, Sally and Peter, can be listed on a ballot paper.
A bag contains four marbles - red, green, blue and yellow. Beth randomly selects a marble, returns the marble to the bag and selects another marble.
Construct a tree diagram for the experiment given.
Find the probability of Beth selecting:
A blue and a yellow marble.
A blue followed by a yellow marble.
2 red marbles.
2 marbles of the same colour.
2 marbles of different colours.
Ivan rolled a standard die and then tossed a coin.
Construct a tree diagram to identify the sample space of rolling a standard die and then tossing a coin.
List all the possible outcomes in the sample space.
Find the probability of the result including an odd number.
Find the probability that the result includes a number less than or equal to 5, and a tail.
Every morning, Mae has toast for breakfast. Each day, she either chooses honey or jam to spread on her toast, with equal chance of choosing either one.
Construct a tree diagram for three consecutive days of Mae’s breakfast choices.
State the probability that on the fourth day Mae chooses honey for her toast.
Find the probability that Mae chooses jam for her toast three days in a row.
The proportion of scholarship recipients at a particular university is \dfrac{7}{10}. The number of students at the university is so large that even if a student is removed, we can say that the proportion of scholarship recipients remains the same. When selecting three students at random, the probability that they are a scholarship recipient or not is presented in the following tree diagram:
Find the probability that all three of the students is a scholarship recipient.
Find the probability that at least one of the students is a scholarship recipient.
Find the probability that at least one of the students is a nonrecipient.
Find the probability there is at least one recipient and one nonrecipient in the selection.
Han plays three tennis matches. In each match, he has \dfrac{3}{5} chance of winning. When playing three matches in a row, the probability that he wins or not is presented in the following tree diagram:
Find the probability that he will win all his matches.
Find the probability that he will lose all his matches.
Find the probability that he will win more matches than he loses.
A bucket contains 5 green buttons and 7 purple buttons. Two buttons are drawn in succession from the bucket. The first button is replaced before the second button is drawn.
Complete the table with the probabilities matching the edges of the probability tree:
| A | B | C | D | E | F |
|---|---|---|---|---|---|
| \dfrac{5}{12} |
Find the probability of drawing two purple buttons.
Sandeep owns four green ties and three blue ties. He selects one of the ties at random for himself and then another tie at random for his friend.
Complete the table with the probabilities matching the edges of the probability tree:
| A | B | C | D | E | F |
|---|---|---|---|---|---|
| \text{} | \dfrac{3}{7} | \dfrac{2}{6} |
Find the probability that Sandeep selects a blue tie for himself.
Calculate the probability that Sandeep selects two green ties.
Bart is purchasing a plane ticket to Adelaide. He notices there are only 4 seats remaining, 1 of them is a window seat \left(W\right) and the other 3 are aisle seats \left(A\right). His friend gets on the computer and purchases a ticket immediately after him. The seats are randomly allocated at the time of purchase.
Fill in the probabilities matching the edges of the probability tree for the seat Bart receives and the seat his friend receives:
| A | B | C | D | E |
|---|---|---|---|---|
| \text{} |
Find the probability that Bart's friend has an aisle seat.
Find the probability of Bart's friend receiving an aisle seat if Bart has a window seat.
A sailor has four meal packets to choose from on her last day but only wants to eat three meals. Two of the packets are oatmeal \left(O\right) and two of them are toasted muesli \left(T\right). She will eat three of them throughout the day, chosen at random. The probability tree shows the options for the day.
Fill in the probabilities matching the edges of the probability tree:
| A | B | C | D | E | F |
|---|---|---|---|---|---|
| \text{} |
Find the probability that she has the same type of meal for breakfast and lunch.
An archer has three arrows that each have a probability of \dfrac{1}{5} of striking a target. If all three arrows are shot at a target:
Construct a tree diagram with the probability on each branch.
Find the probability that all three arrows will hit the target.
Find the probability that at least one arrow will miss the target.
Find the probability that at least one arrow will hit the target.
Hermione is drawing 2 cards from a deck of 52 cards. She draws the first card and checks whether it is red (R) or black (B). Without replacing her first card she draws the second card and records its colour.
Construct a tree diagram of this situation with the probability on each branch.
What is the probability that Hermione draws a black card and then a red card?
For the following, determine if the event has an equal probability to drawing a black then a red card. Answer with Yes or No.
Drawing a red card and then a black card.
Drawing a red card and then another red card.
Drawing a black card and then another black card.
Drawing one black card and one red card in any order.
Drawing at least one black card.
Each school day, Neil either rides his bike to school or walks. There is a 70\% chance Neil will ride his bike.
Construct a probability tree diagram showing Neil’s choices for three consecutive school days.
Find the probability that on the fourth day Neil walks to school.
Find the probability that Neil walks to school three days in a row.
A coin is tossed, then the spinner shown is spun and either lands on A, B or C.
Segment B is \dfrac{1}{8} of the entire cirle.
Construct a probability tree diagram showing all possible outcomes and probabilities.
Find the probability of landing on tails and the spinner landing on A.
Find the probability of landing on tails, or the spinner landing on A, or both.
For breakfast, Maria has something to eat and drinks a hot drink. She will either eat toast or cereal and will drink tea or Milo.
The chance of Maria making toast is 0.7.
The chance of Maria drinking Milo is 0.4.
Construct a tree diagram illustrating all possible combinations of food and drink Maria can have for breakfast and their associated probabilities.
Find the probability Maria drinks tea and eats toast.
Find the probability Maria drinks tea or eats toast.
One cube has 4 red faces and 2 blue faces, another cube has 3 red faces and 3 blue faces, and the final cube has 2 red faces and 4 blue faces. The three cubes are rolled like dice.
Construct a probability tree diagram that shows all possible outcomes and probabilities.
Find the probability that three red faces are rolled.
Find the probability that more red faces than blue faces are rolled.
Find the probability that only one cube rolls a blue face.
Tracy has three races to swim at her school swimming carnival.
The chance she wins the first one is 0.7 and if she wins, her chance of winning the second is 0.8 but if she loses then her chance of winning the second is 0.4.
If she wins the first two then her chance of winning the third is 0.9.
If she lost the first two then her chance of losing the third is 0.9 .
If she won only one of the first two, her chance of winning the third is 0.6.
Calculate the probability Tracy won all three races. Round your answer to three decimal places.
Calculate the probability Tracy won the third race. Round your answer to three decimal places.