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Which of the following cannot be valid assignment of probability for elementary events or outcomes of sample space $S = {w_1, w_2, w_3, w_4, w_5, w_6, w_7}$:
Which of the following cannot be valid assignment of probability for elementary events or outcomes of sample space $S = {w_1, w_2, w_3, w_4, w_5, w_6, w_7}$:
CBSE | Class 11 | Exercise 33.3 | Maths | Probability | RD Sharma
Which of the following cannot be valid assignment of probability for elementary events or outcomes of sample space $S = {w_1, w_2, w_3, w_4, w_5, w_6, w_7}$:

Solution:

For each event to be a valid assignment of probability,

Each event in sample space should have a probability of less than 1, and the total probability of all occurrences should be exactly equal to 1.

(i) Valid.

As each $P (w_i)$ (for i=1 to 7) lies between 0 to 1 and sum of $P (w_1) =1$

(ii) Valid.

As each $P (w_i)$ (for i=1 to 7) lies between 0 to 1 and sum of $P (w_1) =1$

(iii) Not valid.

As sum of $P (w_i) = 2.8$ which is greater than 1

(iv) Not valid.

As $P (w_7) = 15/14$ which is greater than 1

i

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