Question

Wendy throws a dart at this square-shaped target: Part A: Is the probability of hitting the black circle inside the target closer to 0 or 1? Explain your answer. Part B: Is the probability of hitting the white portion of the target closer to 0 or 1? Explain your answer.

Answer 1

Answer:

A: 0, B: 1

Step-by-step explanation:

You don't really have to do any calculations for this question if you know that a probability that is closer to 0 is very unlikely whereas a probability that is closer to 1 is very likely. From the picture, because there is a lot more white area than black, it would be unlikely to hit the black and likely to hit the white, we know that the probability of hitting the black circle is closer to 0 and the probability of hitting the white portion is closer to 1.

Answer 2

Using the formula for area of a circle, pi*r^2, we can determine that the area of the circle is 3.14159 [units] squared. Meanwhile, the area of the white area can be determined by finding the total area and subtracting the area of the circle. This gives us a total white space of about 96.85841.

Ratio of black to white space: 3:97 (rounded to whole numbers)

Ratio of white to black space: 97:3 (rounded to whole numbers)

This may seem incorrect but that is simply because the image is not drawn to scale.

The thrower has a 3% chance of hitting black and a 97% chance of hitting white. I assume the question makes the assumption that the landing spot is random and that the dart will always hit the target, so with this information we get the following answers.

Part A: Closer to 0

Part B: Closer to 1