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2.3 Probability

2.3 Probability

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Question 105

There are 200 students at a sports academy following a training program. Students can choose to participate in three specific workshops:

  • 115 participate in Nutrition (NNN),
  • 85 participate in Psychology (PPP),
  • 90 participate in Bio-mechanics (BBB),
  • 40 participate in Nutrition and Psychology,
  • 30 participate in Psychology and Bio-mechanics,
  • 45 participate in Nutrition and Bio-mechanics,
  • 10 participate in all three workshops.
a.

Draw a Venn diagram to represent this information.

[4]
b.

A student is selected at random from the program. Find the probability that this student participates in:

none of the three workshops,

[2]
c.

Bio-mechanics only.

[2]
d.

Students who want to specialize in high-performance coaching are exactly those who participate in both Psychology and Bio-mechanics. Given that a randomly chosen student wants to specialize in high-performance coaching,

find the probability that this student participates in all three workshops.

[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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