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Chapter: Probability· Mathematics Part 1 (Algebra)

Do the following activity: find the probability of a randomly selected student of your class wearing spectacles, and decide a sample space to find P(getting an even number).

Do the following activity -

Activity I : Total number of students in your class, n(S) = [ ]
Number of students from your class, wearing spectacles, n(A) = [ ]
Probability of a randomly selected student wearing spectacles, P(A) = [ ]
Probability of a randomly selected student not wearing spectacles, P(B) = [ ]

Activity II : Decide the sample space yourself and fill in the following boxes.

[Figure: a flow chart. Left side: box 'Sample space' → S = {   } → n(S) = [ ]. Right side: box 'The condition for event A is getting an even number' → A = {   } → n(A) = [ ]. Below: ∴ P(A) = [ ]/[ ] = [ ].]

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Answer: The numbers depend on your own class and the experiment you choose. A model response is given below.

Activity I (example: a class of 40 students, of whom 12 wear spectacles)

  • Total number of students in the class, \(n(S) = 40\)
  • Number of students wearing spectacles, \(n(A) = 12\)
  • \(P(A) = \frac{n(A)}{n(S)} = \frac{12}{40} = \frac{3}{10}\)
  • Students not wearing spectacles: \(n(B) = 40 - 12 = 28\), so \(P(B) = \frac{28}{40} = \frac{7}{10}\)

Check: \(P(A) + P(B) = \frac{3}{10} + \frac{7}{10} = 1\) ✓ (a student either wears spectacles or does not).

Activity II (example: a die is rolled once)

  • Sample space: \(S = \{1, 2, 3, 4, 5, 6\}\), so \(n(S) = 6\)
  • Event A: getting an even number, \(A = \{2, 4, 6\}\), so \(n(A) = 3\)
  • \(\therefore P(A) = \frac{n(A)}{n(S)} = \frac{3}{6} = \frac{1}{2}\)

For a die rolled once, P(getting an even number) = \(\frac{1}{2}\).

Doubtly AI · 4 Nov 2026 AI-verified · Nov 2026 Report
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