Example 9 - Chapter 16 Class 11 Probability

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Example 9 Let a sample space be S = { 1, 2,..., 6}.Which of the following assignments of probabilities to each outcome are valid? Outcomes 1 2 3 4 5 6 (a) 1 6 1 6 1 6 1 6 1 6 1 6 S = { 1, 2, 3, 4, 5, 6,} Sum of probability = 1 + 2 + 3 + 4 + 5 + 6 = 1 6 + 1 6 + 1 6 + 1 6 + 1 6 + 1 6 = 6 6 = 1 Assignment of probability is valid Example 9 Outcomes 1 2 3 4 5 6 (b) 1 0 0 0 0 0 \ Sum of probability = 1 + 2 + 3 + 4 + 5 + 6 = 1 + 0 + 0 + 0 + 0 + 0 + 0 = 1 Assignment of probability is valid Example 9 Outcomes 1 2 3 4 5 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 1 2 3 4 5 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 1 2 3 4 5 6 (e) 0.1 0.2 0.3 0.4 0.5 0.6 Sum of probability = 1 + 2 + 3 + 4 + 5 + 6 = 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