Probability of combined events

A bag holds 5 balls, with 3 red balls and 2 blue balls. A ball is chosen at random from the bag and is not put back. If that ball is red, a second ball is then chosen at random from the bag and is not put back. This continues until a blue ball is drawn from the bag.

May/June 2015

A group of people were asked which continent they had visited on their most recent holiday. The results are shown in the table below.

May/June 2015

Box $1$ has $2$ white balls, while Box $2$ contains $4$ white balls and $3$ black balls.

May/June 2016

A bag has $10$ counters in total: $8$ are blue and $2$ are white. Two counters are chosen at random from the bag without replacement.

May/June 2016

A bag contains $n$ balls. 3 of the balls are white. Two balls are selected at random from the bag without replacement.

May/June 2017

A student must choose one humanities subject and two different science subjects. Humanities: Geography (G), History (H), Religious studies (R). Science: Physics (P), Chemistry (C), Biology (B).

May/June 2017

Inside a bag there are twelve lettered tiles that spell TRIGONOMETRY.

May/June 2018

Jim has a $0.7$ chance of taking part in the next match. If Jim does play, the probability that his team wins is $0.8$. If Jim does not play, the probability that his team wins is $0.6$.

May/June 2019

Nima is given these six cards. A shape appears on each card. She chooses two cards at random without replacement.

May/June 2019

Inside the bag are these $9$ letter tiles: I, S, O, S, C, E, L, E, S.

May/June 2022

Yasir commutes to work by car, bus, train or bike.

May/June 2022

The set contains $10$ cards altogether. Each card displays either a square or a triangle. On every card, the shape is coloured either green or red.

May/June 2023

Bags of sweets are placed into boxes.

May/June 2023

January contains $31$ days. Find how many January days you would expect to have a temperature above $14^\circ\text{C}$.

May/June 2024

The bag contains $9$ red counters and $3$ green counters. Lee selects two counters at random from the bag, without replacement.

May/June 2025

The box has $13$ pencils in total. Among them, $4$ are red, $7$ are green and $2$ are yellow. Two pencils are then selected at random from the box without replacement.

May/June 2025

A bag has $4$ black tiles and $6$ white tiles. One tile is picked at random from the bag and then put back. A second tile is then picked at random.

May/June 2025

Paul sits examinations in Maths and Physics. The chance that he passes Maths is 0.7. The chance that he passes Physics is 0.6. The outcomes in each subject are independent of one another.

Oct/Nov 2015

Four cards are labelled $1,2,3$ and $4$. One card is picked at random. Then, from the three cards left, a second card is selected at random. The total of the numbers on the two selected cards is found.

Oct/Nov 2016

Adam has a bag with 9 balls, labelled from 1 to 9. Adam chooses a ball at random from the bag and then puts it back. Find the probability that the ball has an odd number.

Oct/Nov 2017

Bag A has 3 black and 2 white beads. Bag B has 2 black and 4 white beads. A bead is selected at random from Bag A and put into Bag B. Then a bead is selected at random from Bag B.

Oct/Nov 2018

There are two bags of beads. In the first bag, there are $7$ beads altogether, with $3$ red and $4$ white. In the second bag, there are $5$ beads altogether, made up of $2$ red and $3$ blue. A bead is chosen at random from each bag.

Oct/Nov 2020

A bag has 36 balls altogether. There are $n$ red balls inside it. Every remaining ball is green. Esther draws two balls from the bag at random, without replacement.

Oct/Nov 2020

Find the probability that Khalid's first card has an even number on it.

Oct/Nov 2021

George has two bags, and each bag contains black balls as well as white balls. A separate experiment uses counters in three colours.

Oct/Nov 2022

A set of $40$ children is each asked how many books they read in the previous month. Write down the mode.

Oct/Nov 2023

State the probability that the ball is green.

Oct/Nov 2023

Mia has 25 shapes altogether. She sorts them into groups according to their properties. The table gives the number of shapes in each group.

Oct/Nov 2024

These are Mandeep’s $9$ number cards.

Oct/Nov 2024

Luca owns these two fair spinners. Spinner A shows 2, 4, 6, 8. Spinner B shows 1, 1, 3, 5.

Oct/Nov 2025

In a sample of 22 students, they are asked whether they take Economics (E) or History (H). The Venn diagram gives these counts: E only = 7, E∩H = 5, H only = 4, neither = 6.

Oct/Nov 2025