Question

Brenda throws a dart at this square-shaped target:

Answer 1

Answer:

  a. closer to 0

  b. closer to 1

Step-by-step explanation:

(a)

For questions like this, we need to assume that dart landing positions are uniformly distributed across the area. Then the probability of a dart landing in a given area is the ratio of that area to the area of the entire target.

For the purpose of answering "closer to 0 or to 1", an estimate of the probability is sufficient. It is not so close to 1/2 that we need to be extra careful in the computation.

Here, the probability of landing a dart in the black circle is less than the probability of it landing in a 2" square. The ratio of the area of that square to the target area is the square of the ratio of the dimensions, so is ...

  (2/11)² = 4/121 ≈ 1/30.

This is closer to 0 than to 1.

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(b)

Then the proportion of the target that is white is greater than 1 - 1/30 = 29/30, which is much closer to 1 than to zero.

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Additional comment

For the black circle to cover half the target area, it would have to have a diameter of about 8.78 inches. The probability of hitting that black circle will be closer to 0 for any diameter less than 8.78 inches.

  π(8.78/2)² ≈ 11²/2

Answer 2

Answer: See below

Step-by-step explanation:

Area of the square  = l*w = 11*11 = 121  

Area of the circle  = pi r^2 = pi*1^2 =  3.142

Part A

P(hitting the circle) = 3.142 / 121  =  0.026 which is closer to 0.

Part B

P(hitting the outside portion)  = 1 - 0.026 = 0.974 which is closer to 1.