A tiny pebble is dropped onto a square surface. If it is equally likely for the pebble to land anywhere inside the square, what is the probability that all or part of the pebble will come to rest inside the circle? Use 3.14 for, and round your answer to the nearest whole percent. A. 72% B. 75% C. 79% D. 80%

Question

Mathematics

Marin Escobar

23 May, 03:25

A tiny pebble is dropped onto a square surface. If it is equally likely for the pebble to land anywhere inside the square, what is the probability that all or part of the pebble will come to rest inside the circle? Use 3.14 for, and round your answer to the nearest whole percent. A. 72% B. 75% C. 79% D. 80%

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Answers (1)

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Rene Lawson · Answer 1

C. 79%

Step-by-step explanation:

The probability of the pebble inside the circle will depend on the area of the circle. I assume that the circle is inside the square surface and has the diameter (d) the same as the square side (s). If the radius equal to half diameter, the area for the circle will be:

circle area = pi * r * r

circle area = 3.14 * (0.5d) * (0.5d)

circle area=0.785 d^2 = 0.785 s^2

The total area where the stone can land is equal to the square area. The area of the square is:

square area = side * side = s^2

Then the chance for the pebble land on the circle is:

circle area / square area = 0.785 s^2 / s^2 = 0.785 = 79%