An urn contains 7 red, 5 white and 3 black balls. Three balls are drawn randomly one after the other without replacement. If it is known that first ball drawn is red and the second ball drawn is white, then the probability that the third ball drawn is not red is

The range of a discrete random variable $X$ is $\{1,2,3\}$ and the probabilities of its elements are given by $P(X=1)=3 k^3, P(X=2)=2 k^2$ and $P(X=3)=7-19 \mathrm{k}$. Then, $P(X=3)=$

Among every 8 units of a product, one is likely to be defective. If a consumer has order 5 units of that product, then the probability that atmost one unit is defective among them is

Out of the given 25 consecutive position integers, three integers are drawn. If the least integer among given 25 integers is an odd number, then the probability that the sum of the three integers drawn is an even number is