This deep dive covers Complex Problem Example within Probability Problems for GCSE Mathematics. Revise Probability Problems in Probability for GCSE Mathematics with 12 exam-style questions and 5 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 3 of 5 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 3 of 5
Practice
12 questions
Recall
5 flashcards
Complex Problem Example
The Scenario
A bag contains 5 red balls and 3 blue balls. Sarah draws 2 balls without replacement. Meanwhile, Tom flips a fair coin twice.
Find:
(a) The probability Sarah gets 2 red balls
(b) The probability Tom gets at least one head
(c) The probability both (a) and (b) happen
Solution:
(a) Sarah's probability (dependent events):
P(2 red) = P(1st red) × P(2nd red | 1st red)
= 5/8 × 4/7 = 20/56 = 5/14
(b) Tom's probability (independent events):
P(at least one head) = 1 - P(no heads)
P(no heads) = P(TT) = 1/2 × 1/2 = 1/4
P(at least one head) = 1 - 1/4 = 3/4
(c) Both events (independent of each other):
P(both happen) = P(Sarah gets 2 red) × P(Tom gets at least 1 head)
= 5/14 × 3/4 = 15/56