M L Aggarwal Solutions for Exercise 1: Exercise 22

Tickets numbered $3, 5, 7, 9,\dots ,29$  are placed in a box and mixed thoroughly. One ticket is drawn at random from the box. Find the probability that the number on the ticket is a number divisible by $3$ .

A box contains $90$ discs which are numbered from $1$ to $90$ . If one disc is drawn at random from the box, find the probability that it bears a two-digit number
 

A box contains $90$ discs which are numbered from $1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,..., 90$. If one disc is drawn at random from the box, find the probability that it bears a perfect square number.
 

A box contains $90$ discs which are numbered from $1$ to $90$ . If one disc is drawn at random from the box, find the probability that it bears a number divisible by $5$.
 

A box contains $90$ discs which are numbered from $1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ..., 90$. If one disc is drawn at random from the box, find the probability that it bears a prime number less than $30$.

A bag contains $1, 2, 3, 4, 5,...,15$ balls of which some are white balls and some are red balls. If the probability of drawing a red ball is twice that of a white ball, find the number of white balls in the bag.

A bag contains six red balls and some blue balls. If the probability of drawing a blue ball is twice that of a red ball, find the number of balls in the bag.

A bag contains $24$ balls of which $x$ are red, $2x$ are white and $3x$ are blue. A ball is selected at random. Find the probability that it is a white ball.