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2.3 Probability

2.3 Probability

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Question 73

A botanical research station monitors two rare plant species, S1 S_1\,S1​ and S2S_2S2​, for signs of a specific fungal blight. Let A A\,A be the event that species S1 S_1\,S1​ is infected and B B\,B be the event that species S2 S_2\,S2​ is infected. The probabilities of these events are given by

P(A)=x,P(B)=y,P(A∪B)=0.6,P(B∣A)=0.4 P(A) = x, \quad P(B) = y, \quad P(A \cup B) = 0.6, \quad P(B|A) = 0.4 P(A)=x,P(B)=y,P(A∪B)=0.6,P(B∣A)=0.4
a.

Show that

3x+5y=3 3x + 5y = 3 3x+5y=3
[4]
b.

The station also tracks a second pathogen. Let C C\,C be the event that species S2 S_2\,S2​ is infected with this second pathogen. It is known that B B\,B and C C\,C are mutually exclusive such that

P(B∪C)=0.65,P(C)=0.1x+y P(B \cup C) = 0.65, \quad P(C) = 0.1x + y P(B∪C)=0.65,P(C)=0.1x+y

(i) Find a second equation in x x\,x and y y\,y that does not involve fractions.

(ii) Hence find the value of x x\,x and the value of yyy.

[6]
c.

Determine whether or not A A\,A and B B\,B are statistically independent. You must show your working clearly.

[3]
Markscheme

2.3 Probability Questions

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

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.

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