If two dice are thrown simultaneously,then the probability that $1$ comes on the first die is

Let two fair six-faced dice $A$ and $B$ be thrown simultaneously. If $E_1$ is the event that die $A$ shows up $4$,$E_2$ is the event that die $B$ shows up $2$,and $E_3$ is the event that the sum of numbers on both dice is odd,then which of the following statements is $NOT$ true?

Describe the sample space for the indicated experiment: $A$ coin is tossed and a die is thrown.

Four persons can hit a target correctly with probabilities $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}$ and $\frac{1}{8}$ respectively. If all hit at the target independently,then the probability that the target would be hit is:

$A$ and $B$ are two events such that $P(A)=0.54$,$P(B)=0.69$ and $P(A \cap B)=0.35$. Find $P(A \cap B^{\prime})$.

The probability of getting the number $5$ when throwing a fair die is: