Probabilities-And-Data gcse Edexcel

The Probability Scale & Basic Probabilities

What is the probability scale?

• Probability describes the likelihood of something happening

  • In real-life you might use words such as impossible, unlikely and certain

  • In maths we use the probability scale to describe probability

• On the probability scale likelihood is measured by a number between 0 and 1

  • 0 means impossible (i.e. it will never happen)

    • a pig will grow wings and fly

  • Between 0 and 0.5 means unlikely

    • getting a ‘6’ when you roll a fair 6-sided dice

    • getting a ‘6’ when you choose a number between one and a million at random can be described as very unlikely

  • 0.5 means even chance (i.e. it happens 50% of the time)

    • getting ‘heads’ when you flip a fair coin

  • Between 0.5 and 1 means likely

    • a spinner that is three quarters green landing on green

    • not getting a ‘6’ when you choose a number between one and a million at random can be described as very likely

  • 1 means certain (i.e. it will always happen)

    • the sun will rise tomorrow morning

• Probabilities can be given as fractions, decimals or percentages

How do I calculate basic probabilities?

• An outcome is a single possible result of a trial

  • For example:

    • a dice lands on 6

    • a dice lands on 5

• If all possible outcomes are equally likely then the probability for each outcome is the same

  • The probability for each outcome is

  • If there are 50 marbles in a bag then the probability of selecting a specific one is

• An event is an outcome or a collection of outcomes

  • For example:

    • a dice lands on a six (one outcome)

    • a dice lands on an even number (a collection of outcomes)

  • Events can be referred to by capital letters

    • e.g. event A might be ‘a dice lands on an odd number’

    • The probability of event A occurring can be written as P(A)

• If all possible outcomes are equally likely then the probability of an event can be calculated by dividing the number of ‘successful’ outcomes by the total number of possible outcomes

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  • A ‘successful‘ outcome is an outcome belonging to the event

    • e.g. for the event ‘a dice lands on an even number’

    • ‘2’, ‘4’ and ‘6’ are all successful outcomes

  • If there are 50 marbles in a bag and 20 are blue, then the probability of selecting a blue marble is

    • The probability of selecting a particular blue marble is still

• A probability worked out this way is sometimes known as a theoretical probability

• The word ‘fair‘ is used to indicate equally likely outcomes

  • e.g. for tossing a fair coin, heads and tails are equally likely

  • or for rolling a fair dice, each number on the dice is equally likely