Question

Question 1 Which of the following can not be valid assignment of probabilities for outcomes of sample space S = {ω1, ω2, ω3, ω4, ω5, ω6, ω7}



Assignment ω1 ω2 ω3 ω4 ω5 ω6 ω7


(a) 0.1 0.01 0.05 0.03 0.01 0.2 0.6

(b) 1/7 1/7 1/7 1/7 1/7 1/7 1/7

(c) 0.1 0.2 0.3 0.4 0.5 0.6 0.7

(d) -0.1 0.2 0.3 0.4 -0.2 0.1 0.3

(e) 1/14 2/14 3/14 4/14 5/14 6/14 15/14

Class X1 - Maths -Probability Page 403

Answer 1

Concept : for valid assignment , sum of all possibilities of each assignment should be 1 .

(a) sum of all possibilities = 0.1 + 0.01 + 0.05 + 0.03 + 0.01 + 0.2 + 0.6 = 1
Hence, the assignment is valid .

(b) sum of all possibilities = 1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 = 7/7 = 1
Hence, the assignment is valid.

j(c) sum of possibilities = 0.1 + 0.2 + 0.3 + 0.4 + 0.5 + 0.6 + 0.7 = 2.8 > 1
Hence, the assignment is not valid .

(d) sum of possibilities = -0.1 + 0.2 + 0.3 + 0.4 -0.2 + 0.1 + 0.3 = 1
Hence, the assignment is not valid because event can't be negative . .

(E) sum of possibilities = 1/14 + 2/14 + 3/14 + 4/14 + 5/14 + 6/14 + 15/14 = 36/14 > 1
Hence, the assignment is not valid .