Question

Which of the following cannot be valid assignment of probability for elementary events or outcomes of sample space S = {w1, w2, w3, w4, w5, w6, w7}:

Elementary events	W1	W2	W3	W4	W5	W6	W7
(i)	0.1	0.01	0.05	0.03	0.01	0.2	0.6
(ii)	\(\frac{1}{7}\)	\(\frac{1}{7}\)	\(\frac{1}{7}\)	\(\frac{1}{7}\)	\(\frac{1}{7}\)	\(\frac{1}{7}\)	\(\frac{1}{7}\)
(iii)	0.7	0.6	0.5	0.4	0.3	0.2	0.1
(iv)	\(\frac{1}{14}\)	\(\frac{2}{14}\)	\(\frac{3}{14}\)	\(\frac{4}{14}\)	\(\frac{5}{14}\)	\(\frac{6}{14}\)	\(\frac{15}{14}\)

Answer 1

For each event to be a valid assignment of probability, the probability of each event in sample space should be less than 1 and the sum of probability of all the events should be exactly equal to 1 

(i) it is valid as each P(w_i) (for i=1 to 7) lies between 0 to 1 and sum of P(w₁) = 1 

(ii) it is valid as each P(w_i) (for i = 1 to 7) lies between 0 to 1 and sum of P(w₁) =1 

(iii) it is not valid as sum of P(w_i)=2.8 which is greater than 1 

(iv) it is not valid as P(w₇) = \(\frac{15}{14}\)  which is greater than 1.