Login/Sign Up
Home » Which of the following cannot be valid assignment of probabilities for outcomes of sample Space ?
Which of the following cannot be valid assignment of probabilities for outcomes of sample Space S{\text{ }} = {\text{ }}\left\{ {{\omega _1},{\text{ }}{\omega _2},{\text{ }}{\omega _3},{\text{ }}{\omega _4},{\text{ }}{\omega _5},{\text{ }}{\omega _6},{\text{ }}{\omega _7}} \right\}?
CBSE | Class 11 | Exercise 16.3 | Maths | NCERT | Probability
Which of the following cannot be valid assignment of probabilities for outcomes of sample Space S{\text{ }} = {\text{ }}\left\{ {{\omega _1},{\text{ }}{\omega _2},{\text{ }}{\omega _3},{\text{ }}{\omega _4},{\text{ }}{\omega _5},{\text{ }}{\omega _6},{\text{ }}{\omega _7}} \right\}?

Given assignment is

(c) Condition (i): Each of the number p\left( {{\omega _i}} \right) is positive and less than zero.

Condition (ii): Sum of probabilities

= {\text{ }}0.1{\text{ }} + {\text{ }}0.2{\text{ }} + {\text{ }}0.3{\text{ }} + {\text{ }}0.4{\text{ }} + {\text{ }}0.5{\text{ }} + {\text{ }}0.6{\text{ }} + {\text{ }}0.7

= {\text{ }}2.8{\text{ }} > {\text{ }}1

Thus, the 2nd condition is not satisfied as p\left( {{\omega _i}} \right) is not \leqslant {\text{ }}1.

Thus, the given assignment is not valid.

(d) The conditions of axiomatic approach don’t hold true in the given assignment, because

(i) Each of the value p\left( {{\omega _i}} \right) is less than zero but also negative.

To be true each of the value p\left( {{\omega _i}} \right) should be less than zero and positive.

Thus, the assignment is not valid.

 

i

More Material