Step 1: Understand equally likely outcomes
Equally likely outcomes refer to situations where each possible outcome has the same probability of occurring.
Step 2: Analyze each option
Option (1): Tossing a coin has two equally likely outcomes: heads and tails.
Option (2): Tossing two coins simultaneously has four equally likely outcomes: (HH, HT, TH, TT).
Option (3): Rolling two dice also has 36 equally likely outcomes, as each die has 6 faces, giving 6 × 6 = 36 possibilities.
Step 3: Conclusion
All of the options represent situations with equally likely outcomes. Hence, the correct option is \( (4) \).
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