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.
\begin{center} \begin{tabular}{|l|c|c|} \hline & Grant awarded (G) & No Grant (G')\\ \hline Biology (B) & 24 & 36 \\ \hline Chemistry (C) & 42 & 28 \\ \hline Physics (P) & 30 & 40 \\ \hline \end{tabular} \end{center}
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.
