A man and his wife appear for an interview for two posts. The probability of the husband's selection is $\frac{1}{7}$ and that of the wife's selection is $\frac{1}{5}$. What is the probability that only one of them will be selected

For independent events ${A_1},\,{A_2},\,..........,{A_n},$ $P({A_i}) = \frac{1}{{i + 1}},$ $i = 1,\,\,2,\,......,\,\,n.$ Then the probability that none of the event will occur, 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.

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 die of red colour, one of white colour and one of blue colour are placed in a bag. One die is selected at random and rolled, its colour and the number on its uppermost face is noted. Describe the sample space.

From a pack of $52$ cards, two cards are drawn one by one without replacement. The probability that first drawn card is a king and second is a queen, is