How many students have got 60% or more marks in all the subjects?
Step 1: Let's assume the marks obtained by students in different subjects are provided as follows:
\[ \begin{aligned} &\text{Student 1: } 85, 60, 70, 80, 75, 90. \\ &\text{Student 2: } 95, 100, 90, 85, 88, 92. \\ &\text{Student 3: } 40, 50, 60, 70, 80, 90. \\ &\text{Student 4: } 60, 55, 65, 70, 60, 75. \end{aligned} \]Step 2: To check whether a student has 60% or more marks in all subjects, we need to see if the student’s marks in each subject are 60 or above.
Thus, only Student 1 and Student 2 qualify.
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