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2.3.2 Conditional probability (A-level only)

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Question 68

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]

2.3.2 Conditional probability (A-level only) Questions

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