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2.3 Probability

2.3 Probability

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Question 131

In a reliability study of an automated irrigation system, two specific failure modes are monitored:

EEE: the system experiences an electrical sensor failure. WWW: the system experiences a water pressure drop.

From historical maintenance data, it is found that:

P(E′∩W)=0.12andP(E′∩W′)=0.68 P(E' \cap W) = 0.12 \quad \text{and} \quad P(E' \cap W') = 0.68 P(E′∩W)=0.12andP(E′∩W′)=0.68
a.

Find P(E)P(E)P(E).

[2]
b.

Find P(E∪W)P(E \cup W)P(E∪W).

[1]
c.

Given that the probability of an electrical failure, given a water pressure drop, is P(E∣W)=0.4P(E|W) = 0.4P(E∣W)=0.4,

calculate P(E∩W)P(E \cap W)P(E∩W).

[3]
d.

Determine, with justification, whether the events EEE and WWW are independent.

[2]
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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