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2.3 Probability

2.3 Probability

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Question 94

An automated safety monitoring system in an industrial plant tracks three types of potential malfunctions: overheating (event AAA), pressure spikes (event BBB), and power surges (event CCC).

For a specific production cycle, it is known that:

P(A)=0.5,P(B)=0.4andP(A∩B)=0.15 P(A) = 0.5, \quad P(B) = 0.4 \quad \text{and} \quad P(A \cap B) = 0.15 P(A)=0.5,P(B)=0.4andP(A∩B)=0.15

Find

a.

P(A∪B)P(A \cup B)P(A∪B)

[2]
b.

P(B′∣A′)P(B' | A')P(B′∣A′)

[3]
c.

The probability of a power surge occurring during the cycle is P(C)=0.3P(C) = 0.3P(C)=0.3.

The occurrences of overheating (AAA) and power surges (CCC) are mutually exclusive. The occurrences of pressure spikes (BBB) and power surges (CCC) are independent events.

Find P(B∩C)P(B \cap C)P(B∩C)

[2]
d.

Describe the configuration of a Venn diagram representing events A,B,A, B,A,B, and CCC and state the probabilities associated with each of the six distinct regions.

[4]
e.

Determine P((B∪C)′)P((B \cup C)')P((B∪C)′)

[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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