Sequential dependent events

A question is this type if and only if it involves sampling without replacement or scenarios where probabilities change based on previous outcomes (e.g., balls from bags, weather patterns).

3 questions

OCR S1 2006 June Q2
2 A bag contains 5 black discs and 3 red discs. A disc is selected at random from the bag. If it is red it is replaced in the bag. If it is black, it is not replaced. A second disc is now selected at random from the bag. Find the probability that
  1. the second disc is black, given that the first disc was black,
  2. the second disc is black,
  3. the two discs are of different colours.
OCR S1 2007 June Q4
4 A bag contains 6 white discs and 4 blue discs. Discs are removed at random, one at a time, without replacement.
  1. Find the probability that
    (a) the second disc is blue, given that the first disc was blue,
    (b) the second disc is blue,
    (c) the third disc is blue, given that the first disc was blue.
  2. The random variable \(X\) is the number of discs which are removed up to and including the first blue disc. State whether the variable X has a geometric distribution. Explain your answer briefly.
OCR PURE 2066 Q12
12 The Venn diagram shows the numbers of students studying various subjects, in a year group of 100 students.
\includegraphics[max width=\textwidth, alt={}, center]{68f1107f-f188-4698-934e-8fd593b25418-7_554_910_347_244} 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. \section*{END OF QUESTION PAPER} \section*{OCR} Oxford Cambridge and RSA