Two-Way Table to Probability

A question is this type if and only if it provides a two-way contingency table and asks for probabilities involving unions, intersections, or complements of the categorized events.

4 questions

CAIE S1 2011 November Q2
2 In a group of 30 teenagers, 13 of the 18 males watch 'Kops are Kids' on television and 3 of the 12 females watch 'Kops are Kids'.
  1. Find the probability that a person chosen at random from the group is either female or watches 'Kops are Kids' or both.
  2. Showing your working, determine whether the events 'the person chosen is male' and 'the person chosen watches Kops are Kids' are independent or not.
OCR S1 2014 June Q7
7 The table shows the numbers of members of a swimming club in certain categories.
\cline { 2 - 3 } \multicolumn{1}{c|}{}MaleFemale
Adults7845
Children52\(n\)
It is given that \(\frac { 5 } { 8 }\) of the female members are children.
  1. Find the value of \(n\).
  2. Find the probability that a member chosen at random is either female or a child (or both). The table below shows the corresponding numbers for an athletics club.
    \cline { 2 - 3 } \multicolumn{1}{c|}{}MaleFemale
    Adults64
    Children510
  3. Two members of the athletics club are chosen at random for a photograph.
    (a) Find the probability that one of these members is a female child and the other is an adult male.
    (b) Find the probability that exactly one of these members is female and exactly one is a child.
OCR MEI Paper 2 2022 June Q4
4 A survey of university students revealed that
  • \(31 \%\) have a part-time job but do not play competitive sport.
  • \(23 \%\) play competitive sport but do not have a part-time job.
  • \(22 \%\) do not play competitive sport and do not have a part-time job.
    1. Show this information on a Venn diagram.
A student is selected at random.
  • Determine the probability that the student plays competitive sport and has a part-time job.
    •
    AQA S1 2012 June Q4
    4 A survey of the 640 properties on an estate was undertaken. Part of the information collected related to the number of bedrooms and the number of toilets in each property. This information is shown in the table.
    \multirow{2}{*}{}Number of toilets
    1234 or moreTotal
    \multirow{5}{*}{Number of bedrooms}146140060
    22467230114
    37729916194
    401912348190
    5 or more00117182
    Total77172256135640
    1. A property on the estate is selected at random. Find, giving your answer to three decimal places, the probability that the property has:
      1. exactly 3 bedrooms;
      2. at least 2 toilets;
      3. exactly 3 bedrooms and at least 2 toilets;
      4. at most 3 bedrooms, given that it has exactly 2 toilets.
    2. Use relevant answers from part (a) to show that the number of toilets is not independent of the number of bedrooms.
    3. Three properties are selected at random from those on the estate which have exactly 3 bedrooms. Calculate the probability that one property has 2 toilets, one has 3 toilets and the other has at least 4 toilets. Give your answer to three decimal places.