



641 students have Teachoo Black. What are you waiting for?
Examples
Example 2 Important
Example 3 (i)
Example 3 (ii)
Example 4 Important
Example 5 Important
Example, 6
Example 7
Example, 8 Important
Example 9 Important You are here
Example 10 Important
Example, 11
Example 12 Important
Example 13 Important
Example 14 Important
Example 15 Important
Example 16
Example 17 Important
Examples
Last updated at Feb. 11, 2020 by Teachoo
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