$A$ bag contains $3$ red and $3$ white balls. If two balls are drawn one after another,what is the probability that they are of different colors?

$A$ bag contains $3$ white and $7$ red balls. If a ball is drawn at random,what is the probability that the drawn ball is either white or red?

Let $S$ be a set of $5$ elements and $P(S)$ denote the power set of $S$. Let $E$ be an event of choosing an ordered pair $(A, B)$ from the set $P(S) \times P(S)$ such that $A \cap B = \varnothing$. If the probability of the event $E$ is $\frac{3^p}{2^q}$,where $p, q \in N$,then $p+q$ is equal to

Two dice are thrown and the sum of the numbers appeared on the dice is noted. If $A$ is the event of getting a prime number as their sum and $B$ is the event of getting a number greater than $8$ as their sum,then $P(A \cap \overline{B})=$

If $A, B$ and $C$ are three events of a random experiment with $P(A)=0.4, P(B)=0.3$ and $P(A \cap B)=0.2$,then the probability that neither $A$ nor $B$ occurs 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 one ticket?