A pharmaceutical research company is testing the effectiveness of a new antiviral treatment, therapy TTT. In a clinical trial involving a large cohort of patients, two events were recorded:
Event T T\,T is defined as the patient receiving the antiviral therapy.
Event R R\,R is defined as the patient showing a significant reduction in viral load within 24 hours.
The following table summarises the joint probabilities for these events based on the trial data:
| RRR | R′R'R′ | |
|---|---|---|
| TTT | 0.36 | 0.24 |
| T′T'T′ | 0.12 | 0.28 |
A patient from the trial is selected at random.
(i) Find P(T)P(T)P(T).
(ii) Find P((T∩R)′)P((T \cap R)')P((T∩R)′).
(iii) Find P(R∣T′)P(R | T')P(R∣T′).
Determine whether the events T T\,T and R R\,R are independent. Fully justify your answer.
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.