$A$ bag contains $2$ red,$3$ green,and $2$ blue balls. Two balls are drawn at random. The probability that none of the balls drawn is blue is

$5$ persons $A, B, C, D$ and $E$ are in a queue at a shop. The probability that $A$ and $E$ are always together is:

Out of the first $5$ consecutive natural numbers,if two different numbers $x$ and $y$ are chosen at random,then the probability that $x^4 - y^4$ is divisible by $5$ is

In a certain lottery,$10,000$ tickets are sold and $10$ equal prizes are awarded. What is the probability of not getting a prize if you buy $2$ tickets?

There are four machines and it is known that exactly two of them are faulty. They are tested,one by one,in a random order until both the faulty machines are identified. Then the probability that only two tests are needed is

Two numbers are chosen at random from $\{1, 2, 3, 4, 5, 6, 7, 8\}$ at a time. The probability that the smaller of the two numbers is less than $4$ is