Sampling without replacement tree diagram

Questions involving drawing items from a container without replacement, where probabilities change based on what was previously drawn.

2 questions

Edexcel S1 2006 January Q4
4. A bag contains 9 blue balls and 3 red balls. A ball is selected at random from the bag and its colour is recorded. The ball is not replaced. A second ball is selected at random and its colour is recorded.
  1. Draw a tree diagram to represent the information. Find the probability that
  2. the second ball selected is red,
  3. both balls selected are red, given that the second ball selected is red.
Edexcel S1 2010 January Q1
  1. A jar contains 2 red, 1 blue and 1 green bead. Two beads are drawn at random from the jar without replacement.
    1. In the space below, draw a tree diagram to illustrate all the possible outcomes and associated probabilities. State your probabilities clearly.
    2. Find the probability that a blue bead and a green bead are drawn from the jar.
    3. The 19 employees of a company take an aptitude test. The scores out of 40 are illustrated in the stem and leaf diagram below.
    \(2 \mid 6\) means a score of 26
    07\(( 1 )\)
    188\(( 2 )\)
    24468\(( 4 )\)
    32333459\(( 7 )\)
    400000\(( 5 )\)
    Find
  2. the median score,
  3. the interquartile range. The company director decides that any employees whose scores are so low that they are outliers will undergo retraining. An outlier is an observation whose value is less than the lower quartile minus 1.0 times the interquartile range.
  4. Explain why there is only one employee who will undergo retraining.
  5. On the graph paper on page 5, draw a box plot to illustrate the employees' scores. \includegraphics[max width=\textwidth, alt={}, center]{a0058e3c-046f-4271-aee4-33a74c719e2a-04_611_1596_2006_185}