Edexcel GCSE Maths: Probability

A bag contains $7$7 red counters and $5$5 blue counters. Two counters are taken from the bag at random, one after the other, without replacement.

(a) Work out the probability that both counters are red. (2 marks)

(b) Work out the probability that the two counters are of different colours. (3 marks)

In a class of $30$30 students, $18$18 study French ($F$F), $14$14 study German ($G$G) and $6$6 study both languages.

(a) Work out how many students study neither language. (2 marks)

(b) One of the $30$30 students is chosen at random. Work out $P(F \cap G')$P(F∩G′) — the probability that the student studies French but not German. (2 marks)

A spinner has sections coloured red, green, blue and yellow. The table shows the probabilities of landing on three of the colours.

Colour	Red	Green	Blue	Yellow
Probability	$0.30$0.30	$0.15$0.15	$x$x	$0.25$0.25

(a) Work out the value of $x$x. (2 marks)

(b) The spinner is spun $200$200 times. Work out an estimate for the number of times it lands on red. (2 marks)

The probability that it rains on any given day during a festival is $0.2$0.2, independently of other days.

Work out the probability that it rains on exactly one of the two days of a weekend festival. (3 marks)

A fair six-sided dice is rolled once.

Work out the probability of rolling a prime number. (2 marks)

The probability that a biased coin lands on heads is $0.65$0.65.

Write down the probability that the coin lands on tails. (1 mark)