IB DP Maths: AI HL复习笔记4.4.1 Probability & Types of Events

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?

• If all outcomes are equally likely then probability for each outcome is the sameHow 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?

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:
• • • This is given in the formula booklet
    • This is a useful formula to test whether two events are statistically independent

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