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2.3 Probability

2.3 Probability

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Question 63

A botanical research station monitors a collection of 200 rare orchids for three specific fungal infections. Let R R\,R be the event that an orchid has root rot, L L\,L be the event of leaf spot, and S S\,S be the event of stem rust.

The distribution of infections in the collection is as follows:

  • 18 orchids have only root rot.
  • 14 orchids have only leaf spot.
  • 22 orchids have only stem rust.
  • 7 orchids have root rot and leaf spot but no stem rust.
  • 9 orchids have root rot and stem rust but no leaf spot.
  • 6 orchids have leaf spot and stem rust but no root rot.
  • 4 orchids suffer from all three infections.
  • The remaining orchids are healthy (free from all three infections).

One orchid is selected at random from the collection.

a.

Determine the probability that the orchid does not have stem rust.

[2]
b.

Find P(R∩L∩S′)P(R \cap L \cap S')P(R∩L∩S′).

[1]
c.

Find P(R∪L∪S′)P(R \cup L \cup S')P(R∪L∪S′).

[2]
d.

Calculate the probability that the orchid has at most one type of infection.

[2]
e.

Given that the selected orchid has at most one type of infection, find the probability it has root rot.

[2]
f.

The random variable X X\,X represents the number of different types of infections found on a randomly selected orchid.

Find the expected value E(X)E(X)E(X).

[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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