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.
If the probability distribution is given by:
| X | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| P(x) | 0 | k | 2k | 2k | 3k | k² | 2k² | 7k² + k |
Then find: \( P(3 < x \leq 6) \)
If \(S=\{1,2,....,50\}\), two numbers \(\alpha\) and \(\beta\) are selected at random find the probability that product is divisible by 3 :