Two-item selection from population

Questions involving selecting exactly two items from a finite population without replacement, typically calculating probabilities of outcomes based on the two selections.

3 questions · Moderate -1.0

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OCR MEI AS Paper 2 Specimen Q4
5 marks Moderate -0.8
4 There are four human blood groups; these are called \(\mathrm { O } , \mathrm { A } , \mathrm { B }\) and AB . Each person has one of these blood groups. The table below shows the distribution of blood groups in a large country.
Blood group
Proportion of
population
O\(49 \%\)
A\(38 \%\)
B\(10 \%\)
AB\(3 \%\)
Two people are selected at random from this country.
  1. Find the probability that at least one of these two people has blood group O .
  2. Find the probability that each of these two people has a different blood group.
OCR PURE Q9
4 marks Easy -1.8
In a survey, 50 people were asked whether they had passed A-level English and whether they had passed A-level Mathematics. The numbers of people in various categories are shown in the Venn diagram. \includegraphics{figure_4}
  1. A person is chosen at random from the 50 people. Find the probability that this person has passed A-level Mathematics. [1]
  2. Two people are chosen at random, without replacement, from those who have passed A-level in at least one of the two subjects. Determine the probability that both of these people have passed A-level Mathematics. [3]
SPS SPS SM Statistics 2024 September Q7
4 marks Moderate -0.3
The Venn diagram shows the numbers of students studying various subjects, in a year group of 100 students. \includegraphics{figure_7} 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. [4]