### Probability

goals
A fair coin is tossed once. Write the sample space of the Random Experiment. State whether the sample space if Finite or Infinite.
There are $6$ marbles in a box with numbers from $1$ to $6$ marked on each of them.
Let X denote the number of colleges where you will apply after your result and P(X=x) denote your probability of your getting admission in x number of colleges. It is given that
$P(X=x)=\left[\begin{matrix} Kx & if & x=0 or 1\\ 2Kx & if & x=2\\ K(5-x) & if & x=3 or 4\end{matrix}\right.$
The probability that a certain kind of component will survive a given shock test is $3/4$. Find the probability that among $5$ components tested exactly $2$ will survive.
A pair of dice is thrown. If the sum of numbers that turned up on the two dice is $8$, then the probability that the number then upon the second die is $5$ is ?