Probability & Probability Scale — Notes & Worked ExamplesShow / Hide
Explanation:
Probability measures how likely an event is on a scale from 0 (impossible) to 1 (certain), with 0.5 or 12 (even chance) in the middle. Always write probabilities as fractions, decimals, or percentages — never as ratios or words like “3 out of 10”.
For equally likely outcomes, P(event) = successful outcomestotal possible outcomes. Because all mutually exclusive outcomes add up to 1, the probability that an event does not happen is P(not A) = 1 − P(A).
Example 1: A bag has 5 red, 3 blue, and 4 green counters. One is picked at random. Find: (a) P(blue) (b) P(not red) (c) P(yellow)
Total = 5 + 3 + 4 = 12 counters:
(a) P(blue) = 312 = 14 (b) P(not red) = 712
(c) No yellow counters → P(yellow) = 0
Example 2: In chess, P(Sam wins) = 0.45 and P(draw) = 0.20. Work out P(Sam loses).
Work out A bag contains 7 red counters, 7 blue counters, and 4 green counters. A counter is picked at random. Write down the probability that it is red.
Worked Solution & Answer
Total counters = 18, so P(red) = 718 = 718. B1
Answer:718
Question 2
[1 mark]
Work out A bag contains 7 red counters, 7 blue counters, and 5 green counters. A counter is picked at random. Write down the probability that it is red.
Worked Solution & Answer
Total counters = 19, so P(red) = 719 = 719. B1
Answer:719
Question 3
[2 marks]
Tom has a fair ordinary dice. He rolls the dice once.
(a)On the probability scale below, mark with a cross (×) the probability that Tom gets the number 2[1 mark]
(b)On the probability scale below, mark with a cross (×) the probability that Tom gets a number greater than 4[1 mark]
Worked Solution & Answer
(a)
P(2) = 1/6 (first division on the scale) B1
Answer (a):Mark at 1/6
(b)
Numbers greater than 4 are 5 and 6 ⇒ P(>4) = 2/6 = 1/3 (second division on the scale) B1
Sandeep is designing some 3-sided spinners. He is going to spin each spinner once.
(a)Write a different number on each dotted line so that when the spinner is spun it is **impossible** that the spinner will land on a number greater than 9[1 mark]
(b)Write a different number on each dotted line so that when the spinner is spun it is **certain** that the spinner will land on a multiple of 10[1 mark]
(b)On the probability scale, mark with a cross (×) the probability of this outcome.[1 mark]
Worked Solution & Answer
(a)
Numbers ≤ 9 B1
Answer (a):Three different numbers ≤ 9 (e.g. 1, 2, 3)
(b)
Multiples of 10 B1
Answer (b):Three different multiples of 10 (e.g. 10, 20, 30)
