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 ?