Suppose that we drop a round coin with a diameter of 1 cm onto a gigantic sheet of paper with red lines drawn vertically every 10 cm and blue lines drawn horizontally every 5 cm.
(i) What is the probability the coin will land on a red line?
The coin crosses a line when at least 1/2 of it is through it. So since the red lines are 10 cm apart you would have to add the 0.5 space from the left line and the 0.5 from the right line $\frac{0.5}{10} + \frac{0.5}{10} = \frac{1}{10}$. (This is straight from the solutions, Below is a picture if the 
(ii) Find the probability the coin lands on both a red and blue line.
I was trying to do this but I get $\frac{1}{4}$ which is too big considering in the next question I have to divide this answer with the answer from (i). My reasoning was if horizontal lines were drawn every 5 cm, there would be squares and since this is asking for when the coin crosses BOTH lines I took the area of a small square that would be at each corner which would be (0.5)(0.5) which is 1/4.
(iii) Given the coin has landed on a red line what is the conditional probability it will land on a blue line? Are the two events of landing on a blue line and landing on a red line independent?
