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2.3 Probability

2.3 Probability

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Question 6

For two events R R\,R and SSS,

P(R∩S)=xP(R \cap S) = xP(R∩S)=x, P(R∩S′)=0.18P(R \cap S') = 0.18P(R∩S′)=0.18, P(R′∩S)=0.28P(R' \cap S) = 0.28P(R′∩S)=0.28, P(R′∩S′)=yP(R' \cap S') = yP(R′∩S′)=y

a.

Write down an expression for y y\,y in terms of xxx.

[1]
b.

Given that P(R∣S)=P(R)P(R\mid S)=P(R)P(R∣S)=P(R), show that x2−0.54x+0.0504=0x^{2} - 0.54x + 0.0504 = 0x2−0.54x+0.0504=0.

[3]
c.

Given also that P(R)<0.5P(R) < 0.5P(R)<0.5, find the value of x x\,x and the value of yyy.

[2]
Markscheme

2.3 Probability Questions

  1. A Level
  2. /Maths
  3. /2.3 Probability

200 exam-style questions on OCR A Level Maths 2.3 Probability, covering 2.3.1 Mutually exclusive and independent events, 2.3.2 Diagrams to assist probability calculations, 2.3.3 Conditional probability (A-level only), 2.3.4 Conditional probability from first principles (A-level only), and 2.3.5 Modelling with probability. Each one has a worked solution and a mark scheme showing where the marks go.

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