Two numbers are selected randomly from the set $S = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$ without replacement one by one. The probability that minimum of the two numbers is divisible by $3$ or maximum of the two numbers is divisible by $4$ , is 

Let $E$ and $F$ be two independent events. The probability that both $E$ and $F$ happen is $\frac{1}{12}$ and the probability that neither $E$ nor $F$ happens is  $\frac{1}{2}$ , then a value of  $\frac{{P(E)}}{{P\left( F \right)}}$ is

One card is drawn from each of two ordinary packs of $52$ cards. The probability that at least one of them is an ace of heart, is

Find the probability that the two digit number formed by digits $1, 2, 3, 4, 5$ is divisible by $4$ (while repetition of digit is allowed)

Two dice are tossed. The probability that the total score is a prime number is

Out of $60 \%$ female and $40 \%$ male candidates appearing in an exam, $60\%$ candidates qualify it. The number of females qualifying the exam is twice the number of males qualifying it. A candidate is randomly chosen from the qualified candidates. The probability, that the chosen candidate is a female, is.