OCR GCSE Maths: Probability

A jar contains $4$4 lime sweets and $5$5 orange sweets. Maya takes two sweets at random, one after the other, and eats the first before taking the second, so the sweets are taken without replacement.

(a) Work out the probability that both sweets are lime. (2 marks)

(b) Work out the probability that the two sweets are the same flavour. (3 marks)

A gym surveys $40$40 of its members. Let $W$W be the set of members who use the weights room and $P$P be the set who use the swimming pool. The survey finds that $24$24 members use the weights room, $18$18 use the pool, and $9$9 use both.

(a) Work out the number of members who use neither the weights room nor the pool. (2 marks)

(b) One of the $40$40 members is chosen at random. Work out $P(W' \cap P)$P(W′∩P), the probability that the member uses the pool but not the weights room. (2 marks)

Each morning Tom cycles to college. The probability that his bus connection is on time is $\dfrac{2}{5}$52​, and independently the probability that the college canteen has his favourite roll is $\dfrac{3}{4}$43​.

(a) Work out the probability that on a given morning the bus is on time and the canteen has his roll. (2 marks)

(b) Work out the probability that neither of these happens. (2 marks)

A machine makes electronic components. In a sample of $200$200 components, $12$12 are found to be faulty.

The machine is going to make a batch of $5000$5000 components. Using the sample, work out an estimate for the number of faulty components in the batch. (3 marks)

A bag contains red, green, blue and yellow beads. A bead is taken from the bag at random. The table shows the probability of taking each colour, but the probability for yellow is missing.

Work out the probability of taking a yellow bead. (2 marks)

A fair spinner has $8$8 equal sections numbered $1$1 to $8$8. The spinner is spun once. Write down the probability that it lands on a prime number. (1 mark)