a dart board is a regular octagon divided into regions as shown. suppose that a dart thrown at the board is equally likely to la

Question

2 years ago

14

nd anywhere on the board. what is the probability that the dart lands within the center square?

1 answer:

Arlecino [84] · Answer 1 · 2024-01-11T13:29:33+03:00

The probability that the dart lands in centre is = √2-1.

<h3>What is probability?</h3>

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
The likelihood that an event will occur increases with its probability.
A straightforward illustration is tossing a fair (impartial) coin.
The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.

acc to our question-,

So all the triangles will have 45-90-45 combinations
c sides of triangles = r/2√r/2
Calculate the total area of octagon and the area of central square
Probability = area of square /area of octagon = r2/(r2+r2+22√+r2)r2/(r2+r2+22+r2)
= 1/(2+22√)
take 2 common and multiply and divide by

hence,The probability that the dart lands in centre is = √2-1.

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