The chances to fail in Physics are $20 \%$ and the chances to fail in Mathematics are $10 \%$. What are the chances to fail in at least one subject (in $\%$)?

When two dice are thrown simultaneously,find the probability of the following:
$(1)$ The numbers are the same.
$(2)$ The difference between the numbers is $1$.

In a lottery containing $35$ tickets,exactly $10$ tickets bear a prize. If a ticket is drawn at random,then the probability of not getting a prize is

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

$A$ and $B$ are two events such that $P(A)=0.58$,$P(B)=0.32$ and $P(A \cap B)=0.28$. Then the probability that neither $A$ nor $B$ occurs is

$A$ die is thrown. Find the probability of the following event: $A$ number less than $6$ will appear.