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2.3.3 Conditional probability (A-level only)

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Question 84

An IT security firm analyzes 250 detected cyber-threats over a weekend. Threats are classified into three categories: Malware (MMM), Phishing (PPP), and Denial of Service (DDD).

  • 140 involve Malware,
  • 120 involve Phishing,
  • 105 involve Denial of Service,
  • 65 involve both Malware and Phishing,
  • 55 involve both Phishing and Denial of Service,
  • 45 involve both Malware and Denial of Service,
  • 20 involve all three categories.
a.

Draw a Venn diagram to represent this information.

[3]
b.

A threat is selected at random from the database. Find the probability that this threat involves:

none of the three categories,

[1]
c.

A threat is selected at random from the database. Find the probability that this threat involves:

Denial of Service only.

[1]
d.

Threats categorized as 'Advanced Persistent Threats' (APT) are those that involve both Phishing and Denial of Service. Given that a randomly selected threat is an APT,

find the probability that this threat also involves Malware.

[2]

2.3.3 Conditional probability (A-level only) Questions

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