Chapter 50: Probability

Probability

• If one event has already occured the probability of other events occurring might change
• This is called conditional probability
• The probability that an event X occurs given that an event Y has already occurred is written as P(X/Y)

Using venn diagrams

• You can solve some conditional probability problems using a Venn diagram
• If an event has already occured, then the sample space for the other events is restricted
• These venn diagrams show the outcomes of two events, A and B

Two-way tables

• You might have to work out probabilities from a two-way table
• This table shows how a group of students travel to school

  ## Tree diagrams

• You can use a tree diagram to answer questions involving conditional probability
• A tree diagram shows all the possible outcomes from a series of events and their probabilities
  • The outcome of the first event can sometimes affect the probability of the second
  • You can write the probability for each event on the branch
  • You multiply along the branches to find the probability of each outcome

  ## Golden rules

• Look out for the words replace or put back in a probability question
  • With replacement = probabilities stay the same
  • Without replacement = first probability stays the same while the others change
• Multiply along the branches
• Add up the outcomes

  ## Selection

• Selection can be without replacement
• The two events are not independent
• The probabilities for the second pick change depending on what is picked first