The probability of an event lies between 0 and 1, inclusive. This means: \[ 0 \leq P(\text{Event}) \leq 1 \] Option (A) 0 is a valid probability, representing an impossible event.
Option (B) 1 is a valid probability, representing a certain event.
Option (D) 0.99999 is a valid probability, as it is still within the range [0, 1].
However, option (C) 1.0001 is not a valid probability because it exceeds the upper limit of 1.
The correct option is (C): \(1·0001\)
If A is any event associated with sample space and if E1, E2, E3 are mutually exclusive and exhaustive events. Then which of the following are true?
(A) \(P(A) = P(E_1)P(E_1|A) + P(E_2)P(E_2|A) + P(E_3)P(E_3|A)\)
(B) \(P(A) = P(A|E_1)P(E_1) + P(A|E_2)P(E_2) + P(A|E_3)P(E_3)\)
(C) \(P(E_i|A) = \frac{P(A|E_i)P(E_i)}{\sum_{j=1}^{3} P(A|E_j)P(E_j)}, \; i=1,2,3\)
(D) \(P(A|E_i) = \frac{P(E_i|A)P(E_i)}{\sum_{j=1}^{3} P(E_i|A)P(E_j)}, \; i=1,2,3\)
Choose the correct answer from the options given below: