2.3 Probability
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Question 15
The Venn diagram shows the probabilities associated with three events XXX, Y Y\,Y and ZZZ, representing students choosing to study different languages. The probability of students studying only X X\,X is 0.15, only Y Y\,Y is 0.2, and only Z Z\,Z is 0.4. The intersection X∩Y X \cap Y\,X∩Y is q q\,q and Y∩Z Y \cap Z\,Y∩Z is ppp. Events X X\,X and Z Z\,Z are disjoint. The probability of studying none of these languages is rrr.
a.[1]
Write down the two events that are mutually exclusive.
b.[2]
Given that P(Y∣Z)=0.2P(Y | Z) = 0.2P(Y∣Z)=0.2, find the value of ppp.
c.[4]
Given also that X X\,X and Y Y\,Y are independent, find the values of q q\,q and rrr.
2.3 Probability Questions
200 exam-style questions on OCR (MEI) A Level Maths 2.3 Probability, covering 2.3.1 Calculate the probability of an event, 2.3.2 Complementary events, 2.3.3 Expected frequency of an event, 2.3.4 Diagrams to calculate probabilities, 2.3.5 Mutually exclusive and independent events, 2.3.6 Add probabilities for mutually exclusive events, 2.3.7 Multiply probabilities for independent events, 2.3.8 Mutually exclusive and independent events (notation) (A-level only), 2.3.9 Venn diagrams for probabilities (A-level only), 2.3.10 Conditional probabilities (A-level only), and 2.3.11 Independence via conditional probability (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.