What key words and terminology are used with probability?

• An?experiment?is a repeatable activity that has a result that can be observed or recorded
  • Trials?are what we call the repeats of the experiment
• An?outcome?is a possible result of a trial
• An?event?is an outcome or a collection of outcomes
  • Events are usually denoted with capital letters:?A, B,?etc
  • n(A)?is the number of outcomes that are included in event?A
  • An event can have one or more than one outcome
• A?sample space?is the set of all possible outcomes of an experiment
  • This is denoted by?U
  • n(U) is the total number of outcomes
  • It can be represented as a?list?or a?table

How do I calculate basic probabilities?

• How do I calculate the expected number of occurrences of an outcome?

• Theoretical probability?can be used to calculate the?expected number of occurrences?of an outcome from?n?trials
• If the probability of an outcome is?p?and there are?n?trials then:
  • The expected number of occurrences is?np
  • This?does not mean?that there will?exactly?np?occurrences
  • If the experiment is repeated multiple times then we expect the number of occurrences to average out to be?np

What is the complement of an event?

• The probabilities of all the outcomes?add up to 1
• Complementary events are when there are?two events?and?exactly one?of them will occur
  • One event has to occur but both events can not occur at the same time
• The?complement of event?A?is the event where event?A?does not happen
  • This can be thought of as?not?A
  • What are different types of combined events?

• The?intersection?of two events (A?and?B) is the event where?both?A?and?B?occur
  • This can be thought of as?A?and?B

How do I find the probability of combined events?

• The probability of?A?or?B?(or both) occurring can be found using the formula

• • • A rearranged version is given in the?formula booklet
    • Basically you multiply the probability of?A?by the probability of?B?then happening

What are mutually exclusive events?

• Two events are?mutually exclusive?if they?can not both happen at once
  • For example: when rolling a dice the events “getting a prime number” and “getting a 6” are mutually exclusive
• If?A?and?B?are mutually exclusive events then:
• Complementary events?are mutually exclusive

What are independent events?

• Two events are?independent?if?one occurring does not affect the probability of the other occurring
  • For example: when flipping a coin twice the events “getting a tails on the first flip” and “getting a tails on the second flip” are independent
• If?A?and?B?are independent events then:

How do I find the probability of combined mutually exclusive events?