Step 1: Understand the concept of probability
Probability is a measure of the likelihood of an event occurring. The probability of an event is always a number between 0 and 1, inclusive. That is: \[ 0 \leq P(\text{event}) \leq 1 \] A probability of 0 means the event cannot occur. A probability of 1 means the event will certainly occur.
Step 2: Analyze each option
Option (1): \( \frac{2}{3} \) is a valid probability, as it is a number between 0 and 1.
Option (2): 15% is equivalent to 0.15, which is a valid probability.
Option (3): 0.7 is a valid probability, as it is between 0 and 1.
Option (4): -1.5 is not a valid probability because probabilities cannot be negative.
Step 3: Conclusion
The only option that cannot be a probability is -1.5, as it falls outside the valid range for probabilities.
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