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

Answer 2

Probability measures chance of occurrence of an event. The probability that you do not get 10 points for this case is 0.9463 approximately.

How to find the geometric probability?

When probability is in terms of area or volume or length etc geometric amounts (when infinite points are there), we can use this definition:

• E = favorable event
• S = total sample space

Then:

$P(E) = \dfrac{A(E)}{A(S)}$

where A(E) is the area/volume/length for event E, and similar for A(S).

For this case, the missing image is attached below.

We get 10 points if we hit the dart in that green shaded region.

Thus, we get:

P(getting 10 points) = Area of that green region/ Area of the big square (assuming that we always hit in that big square and all points of the square are equally probable to get hits).

Now, we have:
Area of the green shaded region = Area of smaller sq. - Area of the circle inside it

Area of smaller square = sq. of its sides = $6^2 = 36 \: \rm in^2$

Area of the circle inside = $\pi r^2 = \pi \times \left(\dfrac{6}{2} \right)^2 \approx 28.27 \: \rm in^2$

Thus, we get:

Area of the green shaded region ≈ $36 - 28.27 = 7.73 \: \rm in^2$

Also, we have:

Area of bigger square = $\rm side^2 = 12^2 = 144 \: \rm in^2$

Thus, we get:

$P(\text{getting 10 points}) = P(\text{Hitting in green region}) \approx \dfrac{7.73}{144}\\P(\text{getting 10 points}) \approx 0.0537$

Thus, we have:

$P(\text{Not getting 10 points}) = 1 - P(\text{Getting 10 points}) \approx 1-0.0537\\P(\text{Not getting 10 points}) \approx 0.9463$

Thus, the probability that you do not get 10 points for this case is 0.9463 approximately.

Learn more about geometric probability here:

https://brainly.com/question/24701316