Question

You throw a dart at the board shown. Your dart is equally likely to hit any point inside the square board. Find the probability that you do not get 10 points. Write your answer as a decimal rounded to the nearest thousandth.

Answer 1

The board that makes the question complete is attached with this answer.

Answer:

The probability that you do not get 10 points is 0.913 (To the nearest thousandths).

Step-by-step explanation:

Given that your dart is equally likely to hit any point inside the square board, we are required to find the probability that you do not get 10 points.

This can be obtained by first obtaining the probability of you getting 10 points, and then subtracting it from 1.

The Probability of Success plus The Probability of Failure of an event is always equal to 1.

Let p be the probability of success, and q be the probability of failure. Then

p + q = 1

=> p = 1 - q

And q = 1 - p

From the attached image, we need to find the area of the entire board, and the area of the circle that contains 10.

Area of entire board = 18² = 324

Area of the circle containing 10 = πr² = π(3²) = 9π

Where r is the radius, 3in.

Probability of hitting 10, P(10) = 9π/324

= 0.08727

≈ 0.087 (to the nearest thousandths)

Now, the probability of not hitting 10

= 1 minus probability of hitting 10.

= 1 - 0.087

= 0.913