This page contains a mix of problems associated with GCSE probability – including a look at a sample space problem

Two independent events

Two spinners

Suppose you spin two spinners.

Spinner 1 is split into three equal sections (RED, GREEN and AMBER)

Spinner 2 is split into four equal sections (TWO RED, GREEN and AMBER)

Suppose you win if the two colours are the same

We can represent the outcomes using a two-way table

 Spinner 2 Red Red Green Amber Spinner  1 Red R,R R,R R,G R,A Green G,R G,R G,G G,A Amber A,R A,R A,G A,A

We can count the number of options/outcomes as 12 (because there are twelve outcomes within the table)

We can see

Two dice

Suppose you roll two dice and multiply the numbers to get a score. You win if the answer is a prime number.

We can also represent this in a table

 Dice 2 1 2 3 4 5 6 Dice 1 1 1 2 3 4 5 6 2 2 4 6 8 10 12 3 3 6 9 12 15 18 4 4 8 12 16 20 24 5 5 10 15 20 25 30 6 6 12 18 24 30 36

REMEMBER – ONE IS NOT A PRIME NUMBER!

The number of possible outcomes is 36

The number of prime numbers 6

So

GIVEN A TABLE OF CONTINUOUS DATA – dependent events

The table below shows the times which as class of 17 people ran.

 Running time Frequency 2 5 7 3

1)    A teacher picks out one person at random. What is the probability they ran over 14 seconds?

There are 10 people who ran over 14 seconds so

2)    The teacher picks out two people. What is the probability they both ran under 16 seconds

REMEMBER THAT the FRACTION CHANGES FOR THE SECOND PERSON BECAUSE ONE PERSON HAS ALREADY BEEN PICKED OUT

 Person 1 Under 16 seconds AND Person 2 Under 16 seconds Answer