Misc 3 - A die has two faces each with number '1', three - Using formulae of sets

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  1. Chapter 16 Class 11 Probability
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Misc 3 A die has two faces each with number ‘1’, three faces each with number ‘2’ and one face with number ‘3’. If die is rolled once, determine • P(2) A normal die has 6 faces 1, 2, 3, 4, 5, 6 But in this question die has following 6 faces 1, 1, 2, 2, 2, 3 n(S) = 6 We need to find P(2) There are 3 three 2’s Hence, n(2) = 3 So, P(2) = 𝑛 2﷯﷮𝑛(𝑆)﷯ = 3﷮6﷯ = 𝟏﷮𝟐﷯ Misc 3 A die has two faces each with number ‘1’, three faces each with number ‘2’ and one face with number ‘3’. If die is rolled once, determine (ii) P(1 or 3) Die has faces 1, 1, 2, 2, 2, 3 Now ,P (1 or 3) = P (1) + P(3) Hence, P (1 or 3) = P (1) + P(3) = 2﷮6﷯ + 1﷮6﷯ = 2 + 1﷮6﷯ = 3﷮6﷯ = 𝟏﷮𝟐﷯ Misc 3 A die has two faces each with number ‘1’, three faces each with number ‘2’ and one face with number ‘3’. If die is rolled once, determine (iii) P(not 3) P(not 3) = 1 – P(3) For P(3) There is only one 3’s Hence , n(3) = 1 P(3) = 𝑛(3)﷮𝑛(𝑆)﷯ = 1﷮6﷯ Hence, P(not 3) = 1 – P(3) = 1 – 1﷮6﷯ = 6 − 1﷮6﷯ = 𝟓﷮𝟔﷯

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