A die is loaded in such a way that each odd number is twice as likely to occur as each even number. If $E$ is the event that a number greater than or equal to $4$ occurs on a single toss of the die then $P(E)$ is equal to

$A$ and $B$ are events such that $P(A)=0.42$,  $P(B)=0.48$ and $P(A$ and $B)=0.16 .$ Determine $P (A$ or $B).$

$A , B, C$ try to hit a target simultaneously but independently. Their respective probabilities of hitting targets are $\frac{3}{4},\frac{1}{2},\frac{5}{8}$. The probability that the target is hit by $A$ or $B$ but not by $C$ is

In a hostel, $60 \%$ of the students read Hindi newspaper, $40 \%$ read English newspaper and $20 \%$ read both Hindi and English newspapers. A student is selected at random. If she reads Hindi newspaper, find the probability that she reads English newspaper.

Let $S=\{1,2,3, \ldots, 2022\}$. Then the probability, that a randomly chosen number $n$ from the set $S$ such that $\operatorname{HCF}( n , 2022)=1$, is.

Two students Anil and Ashima appeared in an examination. The probability that Anil will qualify the examination is $0.05$ and that Ashima will qualify the examination is $0.10 .$ The probability that both will qualify the examination is $0.02 .$ Find the probability that Both Anil and Ashima will not qualify the examination.