Probability

In a class of 40 students, 22 study French, 15 study Spanish and 7 study both. (a) Draw/describe a Venn diagram. (b) A student who studies French is chosen at random. Find the probability that they also study Spanish.

A bag contains 4 red and 6 blue counters. Two counters are taken at random without replacement. Work out the probability that they are the same colour.

A spinner is spun 200 times and lands on red 64 times. (a) Work out the relative frequency of red. (b) Estimate how many times it will land on red in 500 spins. (c) Explain whether the spinner is likely to be fair if it has 4 equal sections.

The probability that a biased coin lands on heads is 0.18. The coin is thrown 350 times. Work out the expected number of heads.

A bag contains 7 red and 5 blue counters. Two counters are taken at random without replacement. Work out the probability that they are the same colour.

400 people took a driving test. 55% passed first time. Of those who failed first time, 40% passed second time. How many people passed on their second attempt?

In a survey of 200 people: 90 are under 30. Of these, 72 use social media daily. Of the people aged 30 or over, 44 use social media daily. (a) Complete a two-way table. (b) A daily user is chosen at random. Find the probability they are under 30.