Let a sample space be `S = {omega_1,omega_2, .... ,omega_6}`. Which of the following assignments of probabilities to each outcome are valid?

Explanation

(a) Condition (i): Each of the number p(omega_i) is positive and less than one.
Condition (ii): Sum of probabilities
`=1/6+1/6+1/6+1/6+1/6+1/6+1/6=1`Therefore, the assignment is valid
(b) Condition (i): Each of the number `p(omega_i)` is either 0 or 1.
Condition (ii) Sum of the probabilities `= 1 + 0 + 0 + 0 + 0 + 0 = 1`
Therefore, the assignment is valid
(c) Condition (i) Two of the probabilities `p(omega_5) and p(omega_6)` are negative, the assignment is not valid
(d) Since `p(omega_6) =3/2 gt 1`, the assignment is not valid
(e) Since, sum of probabilities `= 0.1 + 0.2 + 0.3 + 0.4 + 0.5 + 0.6 = 2.1`, the assignment is not valid.