A cybersecurity firm analyzed 120 security incidents recorded in a single month. Each incident was categorized by its severity level: Low (LLL), Medium (MMM), or High (HHH). The firm tracked four specific types of threats: Phishing, Malware, DDoS, and Data Breach. The total counts for each severity category were 30 incidents of Low severity, 50 of Medium severity, and 40 of High severity. The occurrences are detailed in the table below:
Threat CategoryLow severity (L)Medium severity (M)High severity (H)Phishing81222Malware101518DDoS253510Data Breach587 \begin{array}{|l|c|c|c|} \hline \text{Threat Category} & \text{Low severity } (L) & \text{Medium severity } (M) & \text{High severity } (H) \\ \hline \text{Phishing} & 8 & 12 & 22 \\ \hline \text{Malware} & 10 & 15 & 18 \\ \hline \text{DDoS} & 25 & 35 & 10 \\ \hline \text{Data Breach} & 5 & 8 & 7 \\ \hline \end{array} Threat CategoryPhishingMalwareDDoSData BreachLow severity (L)810255Medium severity (M)1215358High severity (H)2218107Determine the probability that a randomly selected security incident from this study: (i) is a Malware threat and has High severity; (ii) is a DDoS threat; (iii) is a Phishing threat, given that it has Medium severity.
For the incidents classified as Low severity, explain why the events 'is a Malware threat' and 'is a DDoS threat' are not mutually exclusive.
116 exam-style questions on OCR A Level Maths 2.3.3 Conditional probability (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.