Probability worksheet — GCSE Foundation

1.A bag contains 3 red counters, 2 blue counters and 2 green counters. One counter is taken at random from the bag. Work out the probability that the counter is red.

2.An archer hits the bullseye with probability 0.24 on any one shot. She wants to know how many shots she must take to expect to hit the bullseye 12 times. Work out how many shots this is.

3.At a leisure centre, 50 members are asked which activities they do. 32 do yoga, 24 do pilates, and 11 do both. Work out how many members do yoga only, and not pilates.

4.A fair six-sided dice is rolled once. Write down the probability of rolling a 6.

5.Spinner A is numbered 1 to 3 and Spinner B is numbered 1 to 5. Both spinners are spun once, and every outcome is listed as a pair, one number from each spinner. Work out how many equally likely outcomes there are in total.

6.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.

7.Kwame flips a fair coin three times and writes down what it lands on each time. Work out the probability that it lands on heads all three times.

8.Two pupils each flip the same coin to estimate the probability of heads. Leah flips it 40 times and gets 24 heads. Ben flips it 60 times and gets 33 heads. By combining both pupils' results, work out the relative frequency of heads, giving your answer as a fraction in its simplest form.

9.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?

10.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.

11.A spinner has equal sections, and the probability that it lands on blue in a single spin is 1/4. It is spun twice, and the two spins are independent. Work out the probability that it lands on blue on both spins.

12.A sorting office processes 2,000 letters addressed to one postcode area in a week. The probability that a letter is a bill is 0.15. Work out how many of the letters you would expect to be bills.

13.80 people are asked whether they drink tea and whether they drink coffee, and the results are recorded on a frequency tree. The first pair of branches splits the 80 people into 50 tea drinkers and 30 non-tea-drinkers. Of the 50 tea drinkers, 32 also drink coffee. Of the 30 non-tea-drinkers, 6 drink coffee. Work out n(T ∩ C), the number of people who drink both tea and coffee.

14.A machine produces bolts. In a sample of 250 bolts, 15 are faulty. Work out the relative frequency of a bolt being faulty, giving your answer as a fraction in its simplest form.

15.In a game, Freddie says the probability of winning is 0.45, the probability of drawing is 0.3 and the probability of losing is 0.35, and that all three of his probabilities are correct. Which statement about Freddie's probabilities is correct?