Fatima and John appear in an interview for two vacancies for the same post. The probability of Fatima's selection is $\frac{1}{7}$ and that of John's selection is $\frac{1}{5}.$ What is the probability that none of them will be selected?

A bag contains $8$ marbles of which $3$ are blue and $5$ are red. One marble is drawn at random, its colour is noted and the marble is replaced in the bag. A marble is again drawn from the bag and its colour is noted. Find the probability that the marble will be blue followed by red.

A bag contains $8$ marbles of which $3$ are blue and $5$ are red. One marble is drawn at random, its colour is noted and the marble is replaced in the bag. A marble is again drawn from the bag and its colour is noted. Find the probability that the marble will be blue and red in any order.

A bag contains $8$ marbles of which $3$ are blue and $5$ are red. One marble is drawn at random, its colour is noted and the marble is replaced in the bag. A marble is again drawn from the bag and its colour is noted. Find the probability that the marble will be of the same colour.

An urn contains $7$red and $4$ blue balls. Two balls are drawn at random with replacement. Find the probability of getting $2$ blue balls

An urn contains $7$ red and $4$ blue balls. Two balls are drawn at random with replacement. Find the probability of getting one red and one blue ball

A card is drawn from a well-shuffled deck of $52$ cards. The outcome is noted, the card is replaced and the deck reshuffled. Another card is then drawn from the deck.

What is the probability that the first card is an ace and the second card is a red queen?