4.6 Combined events and conditional probabilityIB Maths: Applications and Interpretation HL: Flashcards

What these 13 flashcards ask

Addition rule for P(A\cup B)?
What does A\cup B mean?
What does A\cap B mean?
What is true if A and B are mutually exclusive?
Formula for P(A\mid B)?
Formula for P(A\cap B) using conditional probability?
Test for independent events?
What does 'given that B' do to the sample space?
On a tree diagram, what do you do along a branch?
On a tree diagram, how do you combine different branches for 'or'?
How do second-stage probabilities change without replacement?
Can mutually exclusive events with non-zero probability be independent?
Is 'or' exclusive in probability?

Exam questions on 4.6 Combined events and conditional probability

In a class of 30 students, 18 study Spanish ( $S$ ), 12 study French ( $F$ ) and 5 study both languages. A student is chosen at random from the class.
Find the probability that a student studies French, given that the student studies Spanish.2 marks
A box contains 4 red and 6 yellow pencils. Two pencils are taken at random from the box, one after the other, without replacement.
Find the probability that the two pencils are of different colours.2 marks
A sports club has 120 members. Of these, 70 play tennis ( $T$ ), 50 play badminton ( $B$ ) and 20 play both sports. A member is chosen at random.
Find the number of members who play neither tennis nor badminton.3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).