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2.3 Probability

2.3 Probability

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Question 155

The Venn diagram illustrates the specialized competencies of 40 researchers in a data science lab. The events are defined as:

PPP: Researcher is proficient in Python

SSS: Researcher is proficient in SQL

BBB: Researcher is proficient in Bioinformatics

Within the universal set of 40 researchers:

  • The number who are proficient in Python only is 11.
  • The number proficient in both Python and SQL is 9.
  • The number proficient in SQL only is 10.
  • The number proficient in Bioinformatics (which has no overlap with Python or SQL) is 8.
  • The number with none of these proficiencies is 2.

Venn diagram for 40 researchers, with overlapping sets P and S and a separate set B.

a.

Identify two of these events that are mutually exclusive. Justify your answer.

[2]
b.

Determine whether or not the events PPP and SSS are independent.

[3]
c.

One researcher is selected at random. Calculate the probability that this person:

is proficient in Bioinformatics,

[1]
d.

is proficient in both Python and SQL.

[1]
e.

Given that this researcher is proficient in Python, find the probability that they are also proficient in SQL.

[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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