Calculate end-outcome probability

A question is this type if and only if it asks for the probability of a specific final outcome by multiplying along branches (e.g., probability of specific sequence of events).

2 questions · Moderate -0.6

2.03b Probability diagrams: tree, Venn, sample space
Sort by: Default | Easiest first | Hardest first
CAIE S1 2003 June Q6
9 marks Moderate -0.8
6 The people living in 3 houses are classified as children ( \(C\) ), parents ( \(P\) ) or grandparents ( \(G\) ). The numbers living in each house are shown in the table below.
House number 1House number 2House number 3
\(4 C , 1 P , 2 G\)\(2 C , 2 P , 3 G\)\(1 C , 1 G\)
  1. All the people in all 3 houses meet for a party. One person at the party is chosen at random. Calculate the probability of choosing a grandparent.
  2. A house is chosen at random. Then a person in that house is chosen at random. Using a tree diagram, or otherwise, calculate the probability that the person chosen is a grandparent.
  3. Given that the person chosen by the method in part (ii) is a grandparent, calculate the probability that there is also a parent living in the house.
CAIE S1 2007 November Q7
10 marks Moderate -0.3
7 Box \(A\) contains 5 red paper clips and 1 white paper clip. Box \(B\) contains 7 red paper clips and 2 white paper clips. One paper clip is taken at random from box \(A\) and transferred to box \(B\). One paper clip is then taken at random from box \(B\).
  1. Find the probability of taking both a white paper clip from box \(A\) and a red paper clip from box \(B\).
  2. Find the probability that the paper clip taken from box \(B\) is red.
  3. Find the probability that the paper clip taken from box \(A\) was red, given that the paper clip taken from box \(B\) is red.
  4. The random variable \(X\) denotes the number of times that a red paper clip is taken. Draw up a table to show the probability distribution of \(X\).