Experimental probability and expected outcomes

9.A spinner has 8 equal sections numbered 1 to 8. It is spun 120 times. How many times would you expect it to land on a number greater than 5?

10.A survey of 500 people found that 175 preferred tea to coffee. What is the experimental probability that a person chosen at random prefers tea?

11.A factory tests 400 light bulbs and finds 12 are faulty. Estimate how many faulty bulbs there would be in a batch of 5000.

12.Match each term with its definition.

13.A fair coin is tossed 10 times, then 50 times, then 200 times. Order the experiments by how close the experimental probability of heads is likely to be to 0.5, from closest to least close.

14.Which of these quantities are needed to calculate the experimental probability of an event? (Select all that apply.)

15.Match each term with its meaning.

16.A fair coin is tossed 20 times, then 100 times, then 1000 times. Order the experiments from the one whose experimental probability of heads is likely to be closest to 0.5 to the one likely to be furthest from 0.5.

17.A spinner is spun 400 times. It lands on green 120 times. Which statements are correct? (Select all that apply.)

18.A bag contains 4 red and 6 blue counters. A counter is taken and replaced 50 times, and a red counter is taken 22 times. Which statements are true? (Select all that apply.)

19.Increasing the number of trials makes the experimental probability a better estimate of the true probability.

20.A fair coin is tossed 60 times. How many heads would you expect?

21.A biased coin has probability 0.4 of landing on heads. If the coin is tossed 150 times, how many heads would you expect?

22.A spinner has 5 equal sections numbered 1 to 5. It is spun 80 times. How many times would you expect it to land on a number greater than 3?

23.A bag contains 3 red and 7 blue counters. A counter is taken and replaced 200 times. How many times would you expect to take a red counter?

24.A factory tests 200 components and finds 10 are faulty. Estimate how many faulty components there would be in a batch of 5000.

25.A biased dice has probability 0.35 of landing on a 2. If the dice is rolled 300 times, how many times would you expect it to land on a 2?

26.The experimental probability of an event is calculated as the number of successful trials divided by the total number of trials.

27.A spinner is spun 500 times and lands on blue 150 times. Which statements are correct? (Select all that apply.)

28.Based on the experimental probabilities, which statement is best supported?

29.A bag contains red and blue counters. A counter is taken, recorded and replaced 300 times. A red counter is taken 84 times. Estimate the number of red counters in the bag if the bag contains 50 counters in total.

30.A factory tests 500 components and finds 20 are faulty. It produces a batch of 12,000 components. Which of the following statements are correct? (Select all that apply.)

31.If an experiment is repeated many times, the experimental probability will always equal the theoretical probability.

32.A fair coin is tossed 10 times, then 100 times, then 1000 times. Order the experiments from the one whose experimental probability of heads is likely to be closest to 0.5 to the one likely to be furthest from 0.5.

33.A survey of 250 people found that 75 preferred tea to coffee. Work out the experimental probability that a person chosen at random prefers tea. Give your answer as a fraction in simplest form.

34.What is the name given to the estimate of a probability found by observation or experiment?

35.Which of these is an advantage of estimating a probability using empirical probability?

36.Which of these is a disadvantage of using empirical probability?

37.The relative frequency of an event is calculated as the number of recorded outcomes of that event divided by the total number of trials.

38.Which phrase is also used as an alternative to 'empirical probability' or 'relative frequency'?

39.What does 'a priori probability' mean?

40.Which of these are true about empirical probability? (Select all that apply.)

41.A fair coin is tossed 80 times. How many heads would you expect?

42.A biased dice has probability 0.25 of landing on a 6. If the dice is rolled 240 times, how many times would you expect it to land on a 6?

43.Complete the sentence about experimental probability.

44.A bag contains 7 red and 3 blue balls. A ball is taken and replaced 200 times. How many times would you expect to take a red ball?

45.What name is given to the experimental probability of an event?

46.In a survey of 80 people, 28 said they preferred tea to coffee. Work out the experimental probability that a person chosen at random prefers tea. Give your answer as a decimal.

47.A biased dice has probability 0.2 of landing on a 3. If the dice is rolled 350 times, how many times would you expect it to land on a 3?

48.A factory tests 250 components and finds 15 are faulty. Estimate how many faulty components there would be in a batch of 4000.

49.A fair dice is rolled 120 times. How many times would you expect to roll a 5?

50.A survey of 250 people found that 75 preferred tea to coffee. Work out the experimental probability that a person chosen at random prefers tea. Give your answer as a decimal.

51.Complete the formula for experimental probability.

52.Complete the formula for experimental probability using the letters m and n.

53.Explain why increasing the number of trials in an experiment improves the estimate of the probability of an event.

54.A bag contains 10 counters, some red and some blue. A counter is taken at random and replaced. This is done 200 times, and a red counter is taken 68 times. Estimate the number of red counters in the bag. Show your reasoning.

55.A fair coin is tossed 10 times and lands on heads 7 times. A student says this proves the coin is biased. Explain why the student may be wrong.

56.A bag contains red and blue counters. A counter is taken, recorded and replaced 500 times. A red counter is taken 210 times. Estimate the number of red counters in the bag if the bag contains 50 counters in total.

57.A fair coin is tossed 20 times and lands on heads 14 times. Explain why this does not necessarily mean the coin is biased.

58.A fair coin is tossed 80 times. How many heads would you expect?

59.A biased dice has probability 0.25 of landing on a 6. If the dice is rolled 240 times, how many times would you expect it to land on a 6?

60.In a survey of 80 people, 28 said they preferred tea to coffee. Work out the experimental probability that a person chosen at random prefers tea. Give your answer as a decimal.

61.A biased dice has probability 0.2 of landing on a 3. If the dice is rolled 350 times, how many times would you expect it to land on a 3?

62.A factory tests 250 components and finds 15 are faulty. Estimate how many faulty components there would be in a batch of 4000.

63.A fair dice is rolled 120 times. How many times would you expect to roll a 5?

64.A survey of 250 people found that 75 preferred tea to coffee. Work out the experimental probability that a person chosen at random prefers tea. Give your answer as a decimal.