Probability worksheet — GCSE Foundation

1.A six-sided dice is rolled 12 times. It lands on a six 4 times. Erin says that the dice must be biased. Which of these is the best comment on Erin's statement?

2.A spinner lands on one of four colours: amber, black, cyan or damson. The probability it lands on amber is 0.18, on black is 0.22 and on cyan is 0.24. Work out the probability that it lands on amber or damson.

3.In a board game Mia moves forward by the total of two ordinary fair dice. Work out the probability that her total is 7. Give your answer as a fraction in its simplest form.

4.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?

5.A fair spinner has 8 equal sections. 3 of the sections are red. The spinner is spun 240 times. Work out how many times you would expect it to land on red.

6.A biased spinner is spun 200 times. It lands on red 70 times, on blue 50 times, and on green 80 times. Using these results, work out the expected number of times the spinner does NOT land on red, in 500 spins of the same spinner.

7.Two cards are dealt one after the other from an ordinary pack of 52 playing cards. The first card is not put back before the second is dealt. The pack contains 4 aces. Work out the probability that neither card is an ace. Give your answer as a product of two fractions.

8.On a Saturday, 2,000 customers go through the tills at a supermarket. The probability that a customer buys a reusable bag is 0.08. Work out how many customers you would expect to buy a reusable bag.

9.A fair six-sided dice is rolled once. Work out the probability that the score is an odd number. Give your answer as a decimal.

10.A fair spinner has 10 equal sections, numbered 1 to 10. The spinner is spun 150 times. Work out how many times you would expect it to land on a number greater than 7.

11.The probability that the Hughes family go away during the summer holidays is 3/7. Work out the probability that they do not go away during the summer holidays.

12.The probability that Oliver's train is delayed on any morning is 0.3. Work out the probability that his train is not delayed.

13.A fair spinner is divided into 5 equal sections, 2 labelled win and 3 labelled lose. Zara spins it twice, and the two spins are independent. Work out the probability that she wins on the first spin and loses on the second spin.

14.A box contains 1 white bead, 4 purple beads and 4 red beads. One bead is taken at random from the box. Work out the probability that the bead is white or purple.

15.A bag contains one red counter and one blue counter. Josh takes a counter, notes its colour, puts it back, then takes a counter again. He draws a tree diagram to show every possible pair of colours. Work out how many outcomes are on his tree diagram.