If we take 8 identical slips of paper and write the number 0 on one of them, the number 1 on three of the slips, the number 2 on three of the slips and the number 3 on one of the slips. These slips are folded, put in a box and roughly mixed. One slip is drawn at random from the box. If X is the random variable denoting the number written on the drawn slip, the variance of X is:

The probability distribution of a ramdom variable $X$ is:

$P(X=x)=\begin{cases}kx^2,& x=1,2,3\\2kx,&x=4,5,6\\0,&\text{otherwise}\end{cases}$ Where $K$ is a constant

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A pair of coins thrown then

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A die is thrown twice and the sum of the numbers appearing is observed to be 6. Then the probability that the number 4 has appeared at least once, is

The value of $P(E)$ is

Probability distribution of random variable X is

Then the value of E(X) is

When the doctor arrives late, what is the probability that he comes by bike?