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Conditional Probabilities in Venn Diagrams

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Question 28

The Venn diagram shows the number of vehicles in a logistics fleet that are equipped with any of three safety technologies: Lane Assist (LLL), Adaptive Cruise Control (CCC), and Night Vision (VVV).

  • The number of vehicles with Lane Assist only is 18.
  • The number of vehicles in the intersection of LLL and CCC only is 12.
  • The number of vehicles with Adaptive Cruise Control only is 20.
  • The number of vehicles in the intersection of CCC and VVV only is 10.
  • The number of vehicles with Night Vision only is 14.
  • There are 6 vehicles in the region outside all three circles.
  • It is given that there is no intersection between LLL and VVV, and the intersection of all three technologies is empty.

One vehicle is selected at random.

Venn diagram for Lane Assist L, Adaptive Cruise Control C and Night Vision V, showing the numbers of vehicles in each region.

a.

Show that the probability that the vehicle is equipped with more than one technology is 1140\frac{11}{40}4011​.

[2]
b.

Find the probability that the vehicle has Lane Assist or Adaptive Cruise Control (or both).

[2]
c.

Write down the probability that the vehicle has both Lane Assist and Night Vision.

[1]
d.

Given that the vehicle has at least one of these technologies,

find the probability that the vehicle has Night Vision.

[2]
e.

Determine whether or not having Adaptive Cruise Control and having Night Vision are statistically independent.

[4]

Conditional Probabilities in Venn Diagrams Questions

  1. A Level
  2. /Maths
  3. /Conditional Probabilities in Venn Diagrams

Practise Edexcel A Level Maths Conditional Probabilities in Venn Diagrams with exam-style questions for A Level Maths. 32 questions, matched to the Edexcel A Level Maths (9MA0) 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