The probability distribution of X is :
| X | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| P(X) | $${{1 - d} \over 4}$$ | $${{1 + 2d} \over 4}$$ | $${{1 - 4d} \over 4}$$ | $${{1 + 3d} \over 4}$$ |
For the minimum possible value of d, sixty times the mean of X is equal to _______________.
Let S = {E1, E2, ........., E8} be a sample space of a random experiment such that $$P({E_n}) = {n \over {36}}$$ for every n = 1, 2, ........, 8. Then the number of elements in the set $$\left\{ {A \subseteq S:P(A) \ge {4 \over 5}} \right\}$$ is ___________.
If the probability that a randomly chosen 6-digit number formed by using digits 1 and 8 only is a multiple of 21 is p, then 96 p is equal to _______________.
In an examination, there are 10 true-false type questions. Out of 10, a student can guess the answer of 4 questions correctly with probability $${3 \over 4}$$ and the remaining 6 questions correctly with probability $${1 \over 4}$$. If the probability that the student guesses the answers of exactly 8 questions correctly out of 10 is $${{{{27}k}} \over {{4^{10}}}}$$, then k is equal to ___________.