$A$ bag contains $6$ white and $4$ black balls. Two balls are drawn at random. The probability that they are of the same colour is . . . . . .

Four numbers are chosen at random from $\{1, 2, 3, \ldots, 40\}$. The probability that they are not consecutive is:

There are $10$ engineering colleges and five students $A, B, C, D, E$. Each of these students received an offer from all of these $10$ engineering colleges. They randomly choose a college independently of each other. The probability that all get admission in different colleges can be expressed as $\frac{a}{b}$,where $a$ and $b$ are co-prime numbers. Then the value of $a + b$ is:

$A$ sample of $4$ items is drawn at random without replacement from a lot of $10$ items containing $3$ defective items. If $X$ denotes the number of defective items in the sample,then $P(0 < X < 3)$ is equal to:

The probability that the three cards drawn from a pack of $52$ cards are all red is

Two cards are drawn at random from a well-shuffled pack of $52$ cards. Find the probability that one card is a prime number and the other is a multiple of $5$.