A two-faced fair coin has its faces designated as head $$(H)$$ and tail $$(T)$$. This coin is tossed three times in succession to record the following outcomes: $$H, H,H.$$ If the coin is tossed one more time, the probability (up to one decimal place ) of obtaining $$H$$ again, given the previous realizations of $$H, H$$ and $$H$$, would be _____.

The analysis of a water sample produces the following results: The total hardness (in mg/L as $${\mathrm{CaCO}}_3$$) of the water sample is ______.

The figure shows a U-tube having a 5 mm × 5 mm square cross-section filled with mercury (specific gravity = 13.6) up to a height of 20 cm in each limb (open to the atmosphere).

If 5cm³ of water is added to the right limb, the new height (in cm, up to two decimal places) of mercury in the LEFT limb will be______

A catchment is idealized as a 25 km × 25 km square. It has five rain gauges, one at each corner and one at the center, as shown in the figure. During a month, the precipitation at these gauges is measured as G₁ = 300 mm, G₂ = 285 mm, G₃ = 272 mm, G₄ = 290 mm and G₅ = 288 mm. The average precipitation (in mm, up to one decimal place) over the catchment during this month by using the Thiessen polygon method is_______ .