Listing Outcomes (Edexcel IGCSE Maths)

Systematic Lists

Spec point — 6.3F

When do I need to use lists?

• Lists are needed in probability to show all the possible outcomes

  • This is called the sample space

• Sometimes the lists can be simple

  • For example, the outcomes of flipping a coin are heads or tails (the list is: H, T)

• If there are two sets of outcomes, a grid can be used to list all possibilities

  • For example, rolling two six-sided dice and adding their scores

    • This is called a sample space diagram

What is a systematic list?

• A systematic list is a list that has been created using a rule (or an order) that ensures no outcome is missed

  • The list appears as organised
  • This list is not put together in a random order

• For example

  • The outcomes of rolling a six-sided dice are 1, 2, 3, 4, 5, 6

    • This is in numerical order so it is a systematic list

  • The grid mentioned above (sample space diagram) is a form of systematic listing

    • The grid structure ensures no outcome is missed

How do I list outcomes systematically?

• To list outcomes systematically, you may need to **create your own rules **that cover every possible outcome

• This is common when there are** three (or more) sets of outcomes**

  • You must list all the possibilities by hand

• For example, write out the outcomes from flipping three coins

  • One strategy is to

    • first list the possibilities of having all the same outcomes: HHH, TTT
    • then list the possibilities of "1 tail, 2 heads": THH. HTH. HHT
    • Then list the possibilities of "2 tails, 1 head": TTH. HTT. THT
    • There are 8 outcomes in total: HHH, TTT, THH. HTH. HHT, TTH. HTT. THT

  • Another strategy is to list the outcomes of two coins (HH, HT, TH, TT) then add H or T to each one

    • HH(H), HH(T), HT(H), HT(T), TH(H), TH(T), TT(H), TT(T)

Worked Example Write out all the ways to arrange the letters A, B and C.

Answer:

You need to come up with a systematic way of listing the arrangements One way is to begin by fixing the letter A and rearranging the other letters

A B C or A C B

Then fix the letter B and rearrange the other letters

B A C or B C A

Then fix the letter C and rearrange the other letters

C A B or C B A

Final answer: The six arrangements are ABC, ACB, BAC, BCA, CAB and CBA