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Test: Theoretical and experimental probability

This test distinguishes theoretical probability from experimental probability and calculates the likelihood of events. Tasks cover complementary events, multistage experiments, observed frequencies and the effect of increasing the number of trials.

Question qty: 10
Duration in minutes: 17
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Sample questions

  • A box has r red and b blue balls. Two are drawn without replacement. What is the probability both are red?
  • An experiment is repeated n times and event probability is p%. About how many occurrences are expected?
  • A fair six-sided die is rolled. What is the probability of rolling at most n?
  • What do probabilities 0 and 1 mean?
  • As the number of trials grows, how does experimental probability usually behave?
  • The probability of A is p%. What is the probability of its complement?
  • In n trials, an event occurred s times. Find the experimental probability.
  • A fair coin is tossed n times. What is the probability of heads every time?

Theoretical and experimental probability

For a finite sample space of equally likely outcomes, theoretical probability P(A) is the number of favourable outcomes divided by the total number of outcomes. A probability is always between 0 and 1.

Results of trials

Experimental probability is the relative frequency of an event. As the number of independent trials grows, it generally approaches the theoretical probability but need not equal it exactly. Describe the sample space and verify that its outcomes are equally likely before using simple counting.

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