Probability of combined events

Ravi uses a biased 5-sided spinner, labelled 1 to 5. The table gives the probability for each number.

Feb/March 2017

Samira and Sonia each have a bag that contains 20 sweets. Each bag has 5 red, 6 green and 9 yellow sweets.

Feb/March 2018

Sushila, Ravi and Talika each own a bag of balls, and every bag has 10 red balls together with 8 blue balls.

Feb/March 2019

Suleika is given six cards labelled 1 to 6.

Feb/March 2020

Calculate how many of these 16500 people are expected to use their voucher.

Feb/March 2021

A bag holds 2 green buttons, 5 red buttons and 6 blue buttons. Two buttons are chosen at random from the bag without replacement.

Feb/March 2024

State how many televisions the shop sells on Monday.

Feb/March 2024

Mai purchases two batteries. The probability that a battery is faulty is $\frac{1}{10}$.

Feb/March 2025

In a bag, Gareth has $8$ sweets altogether. Of these, $4$ sweets are orange flavoured, $3$ are lemon flavoured and $1$ is strawberry flavoured.

May/June 2015

The seven cards are A, A, A, A, B, B, C.

May/June 2015

The tree diagram displays the chances of a cricket team either winning or losing its first two matches. In the first match, win $\frac{1}{3}$, lose $\frac{2}{3}$. In the second match, when the first match is a win: win $\frac{3}{4}$, lose $\frac{1}{4}$. In the second match, when the first match is a loss: win $\frac{3}{4}$, lose $\frac{1}{4}$.

May/June 2016

Kiah takes part in a game in which a coin is thrown onto a circular board. Points depend on the region where the coin lands. If the coin lands on a line or fails to reach the board, then 0 points are awarded. The diagram shows concentric regions labelled 20 in the centre, 10 in the middle, and 5 on the outside. The table gives the probabilities of Kiah scoring points on the board from one throw.

May/June 2016

Coins are inserted into a machine when paying to park cars. The chance that the machine turns down a coin is 0.05.

May/June 2016

Simon has two boxes of cards. One box contains cards with a single shape on each one, and each shape is either a triangle or a square. The other box contains cards that are either red or blue. Simon randomly selects one card from each box. The probability of choosing a triangle card is $t$. The probability of choosing a red card is $r$.

May/June 2017

Calculate the probability that Pedro scores a goal in each of the next two matches.

May/June 2017

On any morning, the chance of rain is $\frac{2}{3}$. If it rains, the chance that Asha walks to school is $\frac{1}{7}$. If it does not rain, the chance that Asha walks to school is $\frac{4}{7}$.

May/June 2017

Determine the probability that the pen is green.

May/June 2018

The chance that it will rain tomorrow is $\frac{5}{8}$. Provided that it rains, the chance that Rafael goes to school on foot is $\frac{1}{6}$. When it does not rain, the chance that Rafael walks to school is $\frac{7}{10}$. The diagram shown is a tree diagram, with branches marked Rains / Does not rain and Walks / Does not walk, and the probabilities are left to be filled in.

May/June 2018

The diagram illustrates two card sets. Set A includes: 1, 1, 2, 2, 2. Set B includes: 0, 1, 1, 1, 2.

May/June 2018

Andrei's chance of cycling to school is $r$.

May/June 2019

Complete the probability expression for Angelo drawing two black counters.

May/June 2019

Inside a bag are 5 red balls and 3 blue balls. Sophie chooses a ball at random, records its colour, and then returns it to the bag. She repeats this for a second draw.

May/June 2021

A bag holds 3 blue buttons, 8 white buttons and 5 red buttons. Two buttons are selected at random from the bag, without replacement.

May/June 2021

Malik visits a shop each day to purchase bread. On any day, the chance that Malik goes to the shop in the morning is 0.7. If he goes in the morning, the chance that bread is available for Malik to buy is 0.95. If he goes later, the chance that bread is available for Malik to buy is 0.6.

May/June 2021

Use set notation to give the shaded part of the Venn diagram.

May/June 2022

The spinner has five sides, and the colours are red, blue, green, yellow and orange. The table gives some of the probabilities that the spinner will land on each colour.

May/June 2023

Calculate the probability that one button is green and the other is not green.

May/June 2023

Bag $A$ and bag $B$ each hold red sweets and yellow sweets. Anna chooses one sweet at random from bag $A$, and Ben chooses one sweet at random from bag $B$. The chance that Anna selects a red sweet is $\frac{2}{5}$. The probability that Anna and Ben both select a yellow sweet is $\frac{1}{10}$.

May/June 2023

Maria uses a fair 7-sided spinner numbered 1 to 7.

May/June 2023

Bag $A$ and bag $B$ contain only red counters and blue counters. Stephan selects a counter at random from bag $A$, and Jen selects a counter at random from bag $B$. The probability that Stephan selects a red counter is 0.4. The probability that both Stephan and Jen select red counters is 0.25.

May/June 2024

Complete the timetable

May/June 2024

On the probability scale, add an arrow (↓) to indicate the chance that the spinner stops on 2.

May/June 2024

The diagram displays 7 cards carrying the labels N, A, M, I, B, I, A.

May/June 2024

A box holds 10 counters, and each counter is either red or green. The ratio of red counters : green counters is $1 : 4$. Shareen selects one counter at random, records its colour and replaces it in the box. She then selects a second counter at random. A tree diagram is provided with branches headed First counter and Second counter, and outcomes Red and Green, but the probabilities are blank.

May/June 2025

Stephan has two bags, $A$ and $B$, and each bag contains only red sweets and yellow sweets. He chooses two sweets at random, taking one from bag $A$ and the other from bag $B$. The chance that Stephan chooses a red sweet from bag $A$ is $\frac{3}{5}$. The chance that Stephan chooses a red sweet from bag $A$ and a red sweet from bag $B$ is $\frac{2}{15}$.

May/June 2025

The table gives the chance that a person has blue, brown or green eyes.

Oct/Nov 2015

A box holds 6 red pencils together with 8 blue pencils. One pencil is selected at random and is not put back. Then a second pencil is selected at random. In the tree diagram, several probabilities have been left blank. The probabilities already shown are $\frac{6}{14}$ for choosing red first and $\frac{8}{13}$ for choosing blue second given that red was chosen first.

Oct/Nov 2015

Samira enters two charity runs. The chance that she completes each one is 0.8. A tree diagram shows: First run: completes (0.8) then Second run completes (0.8) or does not complete (0.2); First run does not complete (0.2) then Second run completes (0.8) or does not complete (0.2).

Oct/Nov 2015

A plant has probability $\frac{7}{8}$ of producing flowers. The flowers can be red or yellow. Provided that the plant does produce flowers, the probability that the flowers are red is $\frac{3}{4}$.

Oct/Nov 2016

Sandra has a fair spinner with 8 sides. The spinner shows 3, 4, 4, 4, 5, 5, 6 and 8. Sandra makes two spins and writes down each number it lands on.

Oct/Nov 2016

The sketch depicts two fair dice. The faces on dice $A$ are 0, 0, 1, 1, 1, 3. The faces on dice $B$ are 1, 1, 2, 2, 2, 3. For each roll, the score is the number shown on the upper face.

Oct/Nov 2017

A sample of 200 people was surveyed about which city they would most like to visit next. The table records the results.

Oct/Nov 2018

A box holds 20 packets of potato chips. 6 of the packets are barbecue flavoured. 10 of the packets are salt flavoured. 4 of the packets are chicken flavoured.

Oct/Nov 2018

Bag A has 3 black balls and 2 white balls, whereas bag B has 1 black ball and 3 white balls.

Oct/Nov 2018

Rui has a bag with only 5 black pens, 8 red pens and 3 blue pens inside it. He selects one pen from the bag at random.

Oct/Nov 2019

Harris is sitting a driving test. The result of each attempt does not depend on what happened in earlier attempts. The chance that he passes at the first attempt is 0.6. If he is unsuccessful, the chance that he passes any later attempt is 0.75.

Oct/Nov 2019

Find the probability that both marbles are red.

Oct/Nov 2019

Find the probability that the spinner lands on an even number.

Oct/Nov 2020

The diagram contains six discs. Every disc has one colour and one number. They are labelled as follows: Red 4, Yellow 6, Blue 3, Blue 4, Yellow 2, Blue 3.

Oct/Nov 2020

Those letters form POSSIBILITY.

Oct/Nov 2020

A total of 360 pupils are taking part in a school trip to one of four destinations.

Oct/Nov 2021

The bag contains 5 red balls, 4 blue balls and 3 green balls.

Oct/Nov 2022

Determine how many yellow counters are in the bag.

Oct/Nov 2022

The bag has these cards: 1, 7, 3, 9, 4, 5, 2.

Oct/Nov 2023

Lucia has two fair spinners. Spinner A has 5 equal sections and is labelled 1, 2, 3, 4, 5. Spinner B has 9 equal sections and is labelled 3, 3, 4, 4, 4, 4, 5, 5, 5. Lucia spins both spinners and notes whether each result is a prime number.

Oct/Nov 2023

Work out the amount of milk he uses.

Oct/Nov 2024

Inside the box there are 3 blue pens and 5 red pens.

Oct/Nov 2024

State the probability that the bead is yellow.

Oct/Nov 2024

The bag has 5 white balls together with 3 black balls.

Oct/Nov 2024

On Li’s trip to work, there are 2 sets of traffic lights. The chance that he stops at the first set is 0.4, while the chance that he stops at the second set is 0.7.

Oct/Nov 2025

Bag A has 5 white balls and 3 black balls, whereas bag B has 3 white balls and 1 black ball.

Oct/Nov 2025

Sarah throws a fair 6-sided dice twice.

Oct/Nov 2025

The bag holds red, yellow, blue and green cards. The table lists the probability of drawing a red card and a yellow card. For a blue card or a green card, the probabilities are in the proportion blue : green = 5 : 2.

Oct/Nov 2025

A vase has flowers that are red, pink, or white. Ruth chooses one flower at random from the vase. The probability that the flower is not red is 0.9. The probability that the flower is not pink is 0.65.

Oct/Nov 2025