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2.3 Probability

2.3 Probability

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Question 69

An office manager conducts a survey of 80 employees to determine their morning beverage preferences: Coffee (CCC), Tea (TTT), or Juice (JJJ).

  • No employee drinks both Coffee and Juice.
  • 8 employees drink both Coffee and Tea.
  • 28 employees drink Coffee in total.
  • 32 employees drink Tea in total.
  • 24 employees drink Juice in total.
  • 12 employees do not drink any of these three beverages.

An employee is selected at random from the survey.

a.

Draw a Venn diagram to represent this data.

[3]
b.

State, giving a reason, a pair of mutually exclusive events from C,T, C, T,\,C,T, and JJJ.

[2]
c.

Calculate the probability that the chosen employee drinks exactly two of these beverages.

[2]
d.

Showing your working clearly, determine whether or not the events C C\,C and T T\,T are independent.

[3]
e.

Given that an employee drinks Tea, find the probability that they also drink Juice.

[2]
f.

Find the exact value of P([C∪J]∣T′)P([C \cup J]|T')P([C∪J]∣T′).

[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.

Question bank