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Example 9 - Let sample space be S = {W1, W2,.. W6}. Which  - Basic Formula

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  1. Chapter 16 Class 11 Probability
  2. Serial order wise
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Example 9 Let a sample space be S = {ω1, ω2,..., ω6}.Which of the following assignments of probabilities to each outcome are valid? Outcomes ω 1 ω 2 ω 3 ω 4 ω 5 ω 6 (a) ﷐1﷮6﷯ ﷐1﷮6﷯ ﷐1﷮6﷯ ﷐1﷮6﷯ ﷐1﷮6﷯ ﷐1﷮6﷯ S = { ω1, ω2, ω3, ω4, ω5, ω6,} Sum of probability = ω1 + ω2 + ω3 + ω4 + ω5 + ω6 = ﷐1﷮6﷯ + ﷐1﷮6﷯ + ﷐1﷮6﷯ + ﷐1﷮6﷯ + ﷐1﷮6﷯ + ﷐1﷮6﷯ = ﷐6﷮6﷯ = 1 ∴ Assignment of probability is valid Example 9 Outcomes ω1 ω 2 ω 3 ω 4 ω 5 ω 6 (b) 1 0 0 0 0 0 \ Sum of probability = ω1 + ω2 + ω3 + ω4 + ω5 + ω6 = 1 + 0 + 0 + 0 + 0 + 0 + 0 = 1 ∴ Assignment of probability is valid Example 9 Outcomes ω1 ω 2 ω 3 ω 4 ω 5 ω 6 (c) ﷐1﷮8﷯ ﷐2﷮3﷯ ﷐1﷮3﷯ ﷐1﷮3﷯ – ﷐1﷮4﷯ – ﷐1﷮3﷯ Probability of any event cannot be negative Hence, this assignment of probability is not valid Example 9 Outcomes ω1 ω 2 ω 3 ω 4 ω 5 ω 6 (d) ﷐1﷮12﷯ ﷐1﷮12﷯ ﷐1﷮6﷯ ﷐1﷮6﷯ ﷐1﷮6﷯ ﷐3﷮2﷯ Probability ﷐3﷮2﷯ is greater than 1 But, Probability cannot be greater than 1 Hence, this assignment of probability is not valid Example 9 Outcomes ω1 ω 2 ω 3 ω 4 ω 5 ω 6 (e) 0.1 0.2 0.3 0.4 0.5 0.6 Sum of probability = ω1 + ω2 + ω3 + ω4 + ω5 + ω6 = 0.1 + 0.2 + 0.3 + 0.4 + 0.5 + 0.6 = 2.1 Sum of probability is greater than 1 ∴ This assignment of probability is not valid

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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