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): \(1·0001\)
Four students of class XII are given a problem to solve independently. Their respective chances of solving the problem are: \[ \frac{1}{2},\quad \frac{1}{3},\quad \frac{2}{3},\quad \frac{1}{5} \] Find the probability that at most one of them will solve the problem.
Two persons are competing for a position on the Managing Committee of an organisation. The probabilities that the first and the second person will be appointed are 0.5 and 0.6, respectively. Also, if the first person gets appointed, then the probability of introducing a waste treatment plant is 0.7, and the corresponding probability is 0.4 if the second person gets appointed.
Based on the above information, answer the following