Probability worksheet — GCSE Higher

1.A weather station records whether it rains each day for 40 days: it rains on 9 of the days and does not rain on the rest. A local forecaster claims that the probability of rain on any day is 0.3. Work out the relative frequency of rain from the recorded data.

2.A doctors' surgery has 400 patients. 3 in every 10 of the patients are over 65 years old. 90 of the patients over 65 and 70 of the patients aged 65 or under had a flu jab. One of the patients who had a flu jab is picked at random. Work out the probability that this patient is over 65.

3.A train company runs 25 trains a day, every day. The probability that any one train is late is 0.08. Work out how many late trains the company should expect over a period of 4 weeks.

4.A fair six-sided dice is rolled 90 times. Work out how many more times you would expect it to land on a number less than 4 than on a 6.

5.A frequency tree records 320 calls to a helpline. The calls first split into calls about billing and calls about technical support. Of the technical support calls, the probability that a call was resolved on the first contact is 0.75. If 180 technical support calls were resolved on the first contact, work out how many calls were about billing.

6.A school buys pens from two suppliers and has 1000 pens in stock. Supplier X provided 70% of the pens and supplier Y provided the other 30%. 2% of supplier X's pens are faulty and 8% of supplier Y's pens are faulty. A pen picked at random from the stock is found to be faulty. Work out the probability that it came from supplier Y. Give your answer as a fraction.

7.A two-way table records 150 customers at a café. 90 of the customers bought a hot drink and the rest did not. 54 of the hot-drink customers also bought a cake. 21 of the customers who did not buy a hot drink bought a cake. Work out the percentage of all 150 customers who bought a cake.

8.A clinic recorded 300 booked appointments using a frequency tree. The first branch splits them into 210 adult appointments and the rest child appointments. Of the adult appointments, 189 were attended and the rest were missed. Of the child appointments, 81 were attended. Work out the probability that a booked appointment, chosen at random from the 300, was missed. Give your answer as a fraction in its simplest form.

9.At a sports centre, 45% of the members are aged under 18. 60% of the members aged under 18 swim each week. 20% of the members aged 18 or over swim each week. Work out the percentage of all the members who swim each week.

10.A Venn diagram shows two sets, P and Q, inside a universal set. n(P) = 34, n(Q) = 27, n(P ∩ Q) = 11, and n(ξ) = 90, where ξ is the universal set. Work out n((P ∪ Q)′), the number of elements in neither P nor Q.

11.At a fête, a game costs £3 to play. The probability of winning is 0.1, and each win pays out £20. 150 people play the game. Work out the fête's expected profit from the game.

12.A game has two independent stages. P(win stage 1) = 0.4, and P(win stage 2) = 0.25. Work out the probability that Ffion wins at least one of the two stages.

13.The probability that Leo wakes up before his alarm is 0.35. The probability that his younger sister wakes up before her alarm, independently of Leo, is 0.28. Work out the probability that neither of them wakes up before their alarm.

14.A factory checked 400 items. A frequency tree splits them into 250 items made by machine A and 150 items made by machine B. On machine A's branch, 15 of the items were faulty. On machine B's branch, 5 of the items were faulty. One of the 400 items is picked at random. Work out the probability that it is faulty. Give your answer as a fraction in its simplest form.

15.A café offers 3 types of sandwich, cheese, ham and egg, and 4 types of drink, tea, coffee, juice and water. A customer chooses one sandwich and one drink at random. Work out the probability that the customer chooses egg and water.