Sequential selection with conditional outcomes

1. The Venn diagram shows the numbers of students studying various subjects, in a year group of 100 students.
\includegraphics[max width=\textwidth, alt={}, center]{a65400d1-fadc-4bc7-ba4b-af2df57e390a-04_551_894_395_169} A student is chosen at random from the 100 students. Then another student is chosen from the remaining students. Find the probability that the first student studies History and the second student studies Geography but not Psychology.
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7. The Venn diagram shows the numbers of students studying various subjects, in a year group of 100 students.
\includegraphics[max width=\textwidth, alt={}, center]{c5ea8584-939f-4627-8f81-bac60233d9a3-16_542_883_459_148} A student is chosen at random from the 100 students. Then another student is chosen from the remaining students. Find the probability that the first student studies History and the second student studies Geography but not Psychology.
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13 Bag A contains 3 black discs and 2 white discs only. Initially Bag B is empty. Discs are removed at random from bag A, and are placed in bag B, one at a time, until all 5 discs are in bag B.

1. Write down the probability that the last disc that is placed in bag B is black.
2. Find the probability that the first disc and the last disc that are placed in bag B are both black.
3. Find the probability that, starting from when the first disc is placed in bag B , the number of black discs in bag B is always greater than the number of white discs in bag B.