A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of red ball, find the number of blue balls in the bag.

In a single throw of two dice, what is the probability of getting

(i) a total of 9

(ii) two aces (ones)

(iii) at least one ace

(iv) a doublet

(v) five on one die and six on the other

(vi) a multiple of 2 on one and a multiple of 3 on the other ?

A ladder rests against a wall at an angle α to the horizontal. Its foot is pulled away from the wall through a distance a, so that it slides a distance b down the wall making an angle β with the horizontal. Show that :

$\dfrac{a}{b} = \dfrac{\text{cos α - cos β}}{\text{sin β - sin α}}$

For the following frequency distribution, draw an ogive and then use it to estimate the median.

For the same distribution, as given above, draw a histogram and then use it to estimate the mode.