Suppose that we drop a round coin with a diameter of 1 cm onto a gigantic sheet

Question

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. (a) What is the probability the coin will land on a red line? (b) Find the probability the coin lands on both a red and blue line. (c) 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?

Explanation / Answer

(a) Diameter of the coin = 1 cm

Width of the area from one red line to another = 10 cm

=> Probability that the coin will land on a red line = 1/10 = 0.1

(b) Diameter of the coin = 1 cm

Length of the area from one red line to another = 5 cm

=> Probability that the coin will land on a red line = 1/5 = 0.2

(c) The two events are indeed independent.

Conditional probability = Probability of landing on the blue line = 0.2

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