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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

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

Condition (ii): Sum of probabilities

0.01{\text{ }} + {\text{ }}0.05{\text{ }} + {\text{ }}0.03{\text{ }} + {\text{ }}0.01{\text{ }} + {\text{ }}0.2{\text{ }} + {\text{ }}0.6{\text{ }} = {\text{ }}1

Thus, the given assignment is valid.

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

Condition (ii): Sum of probabilities

= {\text{ }}\left( {1/7} \right){\text{ }} + {\text{ }}\left( {1/7} \right){\text{ }} + {\text{ }}\left( {1/7} \right){\text{ }} + {\text{ }}\left( {1/7} \right){\text{ }} + {\text{ }}\left( {1/7} \right){\text{ }} + {\text{ }}\left( {1/7} \right){\text{ }} + {\text{ }}\left( {1/7} \right)

= {\text{ }}7/7

= {\text{ }}1

Thus, the given assignment is valid.

i

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