R S Aggarwal and Veena Aggarwal Solutions for Exercise 2: Exercise 19B

A letter is chosen at random from the letters of the word '$\mathrm{ASSOCIATION}$'. Find the probability that the chosen letter is an $\mathrm{S}$. (Write the final answer in its simplest fraction form)

Five cards-the ten, jack, queen, king and ace of diamonds are well shuffled with their faces downwards. One card is then picked up at random. What is the probability that the drawn card is the queen. If the answer is in the form $\frac{a}{b}$, then find the value of $a$.

Five cards-the ten, jack, queen, king and ace of diamonds are well shuffled with their faces downwards. One card is then picked up at random. If a queen is drawn in the first draw and put aside and a second card is drawn. If the probability that the second card is an ace is $\frac{1}{k}$, find $k$.

Five cards - the ten, jack, queen, king and ace of diamonds are well shuffled with their faces downwards. One card is then picked up at random.

If the queen is drawn and put aside and a second card is drawn, find the probability that the second card is a queen.

A card is drawn at random from a well-shuffled pack of $52$ cards. Find the probability that the card drawn is neither a red card nor a queen.

The probability of selecting a rotten apple randomly from a heap of $900$ apples is $0.18$. What is the number of rotten apples in the heap?

A bag contains $15$ white and some black balls. If the probability of drawing a black ball from the bag is thrice that of drawing a white ball. Find the number of black balls in the bag.

Find the probability of getting the sum of two numbers, less than $3$ or more than $11$, when a pair of distinct dice is thrown together.