A gumball machine contains 1568 gumballs. It is filled monthly with America's original Dubble Bubble Gumballs. Each gumball is approximately 2cm in diameter. The original gumballs have a solid colour coating and come in 8 flavours; strawberry, pineapple, blueberry, lemon-lime, orange, cherry, banana and grape. However, the machine also contains Berry Blast Speckled Dubble Bubble Gumballs (and as the name suggests have a speckled or mottled coating). The colours/flavours/coatings in the machine in this particular week are: strawberry (solid red coating), Blueberry (solid blue coating), banana (solid yellow coating), orange (solid orange coating), strawberry (speckled red coating), lemon (speckled yellow coating) and blueberry (speckled blue coating). Six hundred and ninety are speckled and 36.224% are yellow. Of the red ones, 198 have a solid colour coating and 201 are speckled. There are 344 blue solid coated gumballs. Only 3.316% are banana flavoured.

A child inserts a coin into the gumball machine to obtain a single gumball at random. What is the probability of the following events?

I. What is the probability that the child randomly selects a gumball that is orange flavoured and has a solid colour coating?

II. What is the probability that the child randomly selects a gumball with a solid colour coating or one that is flavoured as strawberry?

III. What is the probability that the speckled gumball chosen by the child at random turns out to be strawberry flavoured?

IV. What is the probability that the child randomly obtains an orange coloured gumball?

V. What is the probability that the child randomly selects a lemon flavoured gumball?

VI. What is the probability that the child randomly selects a gumball that is speckled given that it is strawberry flavoured?

VII. What is the probability that the child randomly obtains a solid colour gumball?

VIII. Are the events "strawberry flavoured" and "speckled" independent?