When a die is thrown once, there are 6 possible outcomes, as the die has 6 faces numbered from 1 to 6. When the die is thrown twice, the total number of possible sample events can be found by multiplying the outcomes of the first throw by the outcomes of the second throw. Thus, the number of sample events is: \[ 6 \times 6 = 36 \] Therefore, the number of sample events when a die is thrown twice is 36.
The correct option is (D): \(36\)
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