$A$ card is drawn at random from a pack of $100$ cards numbered $1$ to $100$. The probability of drawing a number which is a perfect square is

If $P(A) = P(B) = x$ and $P(A \cap B) = P(A' \cap B') = \frac{1}{3}$,then $x = $

Two dice are rolled simultaneously. The probability that the sum of the two numbers on the dice is a prime number is:

The events $A$ and $B$ have probabilities $0.25$ and $0.50$, respectively. The probability that both $A$ and $B$ occur simultaneously is $0.14$. Then, the probability that neither $A$ nor $B$ occurs is:

Two dice are rolled. If both dice have six faces numbered $1, 2, 3, 5, 7, 11$,then the probability that the sum of the numbers on the uppermost faces is a prime number is:

$A$ six-faced unbiased die is thrown twice and the sum of the numbers appearing on the upper face is observed to be $7$. The probability that the number $3$ has appeared at least once is: