Conditional probabilityIB MYP Maths Extended: Flashcards

What these 13 flashcards ask

How do you read P(A\mid B)?
Formula for conditional probability?
What does 'given that' do to the sample space?
Are P(A\mid B) and P(B\mid A) always equal?
Formula for P(A and B) using conditional probability?
What are dependent events?
Which kind of selection gives dependent events?
6 ripe and 4 unripe; a ripe is taken. P(second unripe)?
On a tree diagram, what do you do along a path?
On a tree diagram, what do you do with different paths for the same outcome?
In a two-way table, what is the denominator for P(instrument\midYear 10)?
In a Venn diagram, which total do you use for P(S\mid F)?
What does P(A\mid B)=P(A) tell you?

Exam questions on Conditional probability

A school in Nairobi has 80 students in Years 9 and 10 who were asked whether they play a musical instrument. In Year 9, 18 of 40 students play an instrument and 22 do not. In Year 10, 27 of 40 students play an instrument and 13 do not. One student is chosen at random from the 80.
Find the probability that a student who does not play an instrument is in Year 10.2 marks
A student investigates bags that each contain $r$ red counters and 1 blue counter. She picks two counters without replacement and finds the probability that both are red. For $r=2$ it is $\frac13$ , for $r=3$ it is $\frac12$ , for $r=4$ it is $\frac35$ and for $r=5$ it is $\frac23$ .
Use the pattern to find the value of $r$ for which the probability that both counters are red is $\frac{9}{11}$ , and verify your answer by calculating the probability directly.2 marks
A basket in a market in Cairo holds 10 mangoes: 6 are ripe and 4 are unripe. Two mangoes are taken at random without replacement.
Find the probability that the first mango is ripe, the probability that the second is unripe given that the first was ripe, and the probability that the first is ripe and the second is unripe.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).