Probability worksheet — GCSE Higher

1.Dice A is a fair six-sided dice. Dice B is biased so that P(6) = 0.3. Dice A is rolled 150 times and Dice B is rolled 150 times. Work out how many more sixes you would expect from Dice B than from Dice A.

2.In a game, Zara says the probability of scoring is 3/8, the probability of missing is 5/12 and the probability of a rebound is 1/6, and that these are the only three outcomes. Is Zara correct that her three probabilities are valid?

3.An ordinary six-sided dice, numbered 1 to 6, is rolled 30 times and lands on a 6 seven times. Ravi says the theoretical probability of rolling a 6 and the relative frequency of rolling a 6 in this trial are the same number. Is Ravi right?

4.A survey of 160 employees at a company recorded whether they cycle to work, using a frequency tree. The first branch splits them into 90 who work full-time and 70 who work part-time. Of the full-time employees, 27 cycle to work. Of the part-time employees, 14 cycle to work. Work out the probability that an employee, chosen at random from the 160, cycles to work. Give your answer as a fraction in its simplest form.

5.A spinner can land on red, blue, green or yellow. The probability that it lands on red is 0.24 and the probability that it lands on yellow is 0.16. The probabilities of landing on blue and on green are equal, and each is called x. Work out the value of x.

6.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.

7.A factory finds that the probability a randomly chosen light bulb is defective is 0.035. In a batch of 4,000 bulbs, work out how many bulbs you would expect to work correctly.

8.A charity bake sale tracked 240 items sold using a frequency tree. The first branch splits sales into 150 cake sales and 90 biscuit sales. Of the cake sales, 100 were bought by adults and the rest by children. Of the biscuit sales, 54 were bought by children. Each item sold for £1.20. Work out the total amount of money raised from sales to children.

9.A frequency tree records the results of 160 patients who took a new medicine. It splits them into those who reported side effects and those who did not. 15% of the patients reported side effects. Work out how many of the 160 patients did not report side effects.

10.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.

11.A two-way table records how 180 students at a school travel: by bus or on foot, split by year group. There are 84 students in Year 11, of whom 38 travel by bus and the rest walk. The rest of the 180 students are in Year 10, and 42 of the Year 10 students travel by bus. Work out the probability that a randomly chosen Year 10 student walks to school. Give your answer as a fraction in its simplest form.

12.A game uses a fair spinner with 5 equal sections numbered 1 to 5. A player wins £12 if the spinner lands on 5, and wins nothing otherwise. It costs £2 to play. The game is played 250 times. Work out the expected profit for the players, in total, over the 250 games.

13.A fair six-sided dice is rolled 300 times. Work out how many more times you would expect it to land on an even number than on a six.

14.A fair coin is flipped again and again. After the first 10 flips there have been 7 heads. After 1000 flips there have been 528 heads. Which statement best describes what these results show?

15.A test for a medical condition is given to 1000 people. 50 of the people have the condition and 950 do not. The test is positive for 45 of the 50 people who have the condition, and it is also positive for 95 of the 950 people who do not have the condition. One of the people whose test is positive is picked at random. Work out the probability that this person has the condition.