In a scientific research facility with 200 doctoral candidates, researchers are categorized by their primary field: Biology, Chemistry, or Physics. The following table summarizes the distribution of researchers and whether they have been awarded a research Grant or Not.
| Grant awarded (GGG) | No Grant (G′G'G′) | |
|---|---|---|
| Biology (BBB) | 24 | 36 |
| Chemistry (CCC) | 42 | 28 |
| Physics (PPP) | 30 | 40 |
A researcher is selected at random from the facility. Determine:
P(C)P(C)P(C)
P((B∩G)′)P((B \cap G)')P((B∩G)′)
P(G∣P)P(G | P)P(G∣P)
Let A A\,A be the event that a researcher has published a first-author article this year. Given that 30% of Biologists have published a first-author article, 10% of Chemists have published a first-author article, and 20% of Physicists have published a first-author article,
describe the structure of a Venn diagram to represent the events BBB, CCC, P P\,P and AAA.
find the probability that a randomly selected researcher has published a first-author article this year.
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.