Use a contingency table for probability, independence, conditioning and sampling without replacement.

Use a contingency table for probability, independence, conditioning and sampling without replacement.

12 marks
ProbabilityQuestionBank.pdf

The table below shows the subjects studied by 210 students at a college.

Year 1Year 2Totals
History503585
Science153045
Art453580
Totals110100210
  1. A student from the college is selected at random. Let A be the event the student studies Art. Let B be the event the student is in Year 2.[6]
    1. Find \(P(A)\).
    2. Find the probability that the student is a Year 2 Art student.
    3. Are the events A and B independent? Justify your answer.
  2. Given that a History student is selected at random, calculate the probability that the student is in Year 1.[2]
  3. Two students are selected at random from the college. Calculate the probability that one student is in Year 1, and the other in Year 2.[4]

Solution:

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Answer:One from each year has probability \(2\cdot\frac{110}{210}\cdot\frac{100}{209}=0.501\).

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