GCSE / IGCSE Maths – Probability

A biased four-sided spinner has $P(1) = 0.2$ and $P(2) = 0.35$. The probability of landing on $4$ is twice the probability of landing on $3$.(a) Find $P(3)$.(b) The spinner is spun $200$ times. Estimate the number of times it lands on $4$.

Two fair six-sided dice are rolled and the scores are recorded.(a) Find the probability that the sum of the scores is $8$.(b) Find the probability that the product of the scores is $12$.

Events $A$ and $B$ are independent with $P(A) = 0.4$ and $P(B) = 0.5$.(a) Find $P(A \text{ and } B)$.(b) Find $P(A \text{ or } B)$.

Three fair coins are flipped.(a) List all $8$ possible outcomes.(b) Find the probability of getting at least two heads.

A drawing pin is dropped $50$ times and lands point up $16$ times.(a) Write down the relative frequency of landing point up.(b) The pin is dropped $300$ times. Estimate how many times it lands point up.(c) Explain how the estimate of the probability could be made more reliable.

A bag contains $5$ red and $3$ blue counters. Two counters are taken at random without replacement.(a) Draw a tree diagram to show the probabilities.(b) Find the probability that both counters are red.(c) Find the probability that the counters are different colours.

The probability that it rains on a given morning is $0.3$. If it rains, the probability that Amira is late for school is $0.6$. If it does not rain, the probability that she is late is $0.1$.(a) Find the probability that Amira is late for school.(b) Given that Amira is late, find the probability that it rained.

In a class of $40$ students, $22$ study French, $18$ study History and $7$ study both.(a) Draw a Venn diagram to show this information.(b) Find the probability that a student chosen at random studies neither subject.(c) A student who studies French is chosen at random. Find the probability that they also study History.

A box contains $4$ green and $6$ yellow sweets. Two sweets are chosen at random without replacement.Find the probability that at least one sweet is green.

A fairground game costs $\$1$ to play. The probability of winning is $0.15$ and a winner receives $\$5$.(a) Find the expected winnings, in dollars, from one game (ignoring the cost).(b) Show that a player who plays $200$ times can expect to lose $\$50$ overall.

A bag contains $x$ red counters and $6$ blue counters. Two counters are taken at random without replacement. The probability that both counters are blue is $\dfrac{1}{3}$.(a) Show that $(x + 6)(x + 5) = 90$.(b) Hence find the value of $x$.

$60$ people were asked whether they drink tea (T) or coffee (C). $25$ drink only tea, $15$ drink only coffee, $12$ drink both and the rest drink neither.(a) Find how many people drink neither.(b) One person is chosen at random. Find $P(T \cap C)$.(c) A tea drinker is chosen at random. Find the probability that they also drink coffee.(d) Two different people are chosen at random. Find the probability that neither of them drinks tea.