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1.1 OT1: Mathematical argument, language and proof

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An astrophysicist is monitoring a space telescope's imaging sensors for three types of interference: Cosmic Ray hits (CCC), Solar Flares (SSS), and Thermal Noise spikes (TTT). The probabilities of these events occurring during a specific exposure window are provided below using set notation:

  • P(C∩S′)=0.147P(C \cap S') = 0.147P(C∩S′)=0.147
  • P(C∩S)=0.062P(C \cap S) = 0.062P(C∩S)=0.062
  • P(S∩C′∩T′)=0.224P(S \cap C' \cap T') = 0.224P(S∩C′∩T′)=0.224
  • P(S∩T)=0.088P(S \cap T) = 0.088P(S∩T)=0.088
  • P(T∩S′)=0.319P(T \cap S') = 0.319P(T∩S′)=0.319

It is known that the telescope's shielding prevents Cosmic Ray hits and Thermal Noise spikes from occurring simultaneously, making them mutually exclusive events (C∩T=∅C \cap T = \emptysetC∩T=∅).

Given that the probability of an exposure having no interference is represented by www, determine the value of www.

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1.1 OT1: Mathematical argument, language and proof Questions

  1. A Level
  2. /Maths
  3. /1.1 OT1: Mathematical argument, language and proof

Practise AQA A Level Maths 1.1 OT1: Mathematical argument, language and proof with exam-style questions for A Level Maths. 8 questions covering 1.1.1 Constructing mathematical arguments, 1.1.2 Mathematical language and syntax, 1.1.3 Set theory language and symbols, 1.1.4 Definition, domain and range of functions, and 1.1.5 Comprehending and critiquing arguments, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

Question bank