Question

If you are given a paper which has lines which are the length of a needle apart, and then you repeated drop that needle onto the paper, the probability that the needle with cut the line is:

Answer 1

The probability that the needle with cut the line is determined as 1/π. (Option A).

How to calculate the probability?

The probability that the needle with cut the line is calculated by applying the following formula;

Probability that the needle with cut the line = area under the curve / area of rectangle

The area under the curve is calculated as;

`A = \int\limits^(\pi /2)_0 {(1)/(2) sin \theta} \, d \theta`

A = 1/2

The area of the rectangle is calculated as;

A = π/2

The probability that the needle with cut the line is calculated as;

P = (1/2) / (π/2)

P = 2/2π

P = 1/π

Answer 2

The correct option is;

`(1)/(\pi )`

Explanation:

Here we have that

`Probability = (Number \, of \, required\, outcomes)/(Number \, of \, possible\ outcomes) = (Dimension \, of \, the \, line)/(Size \, of \, the \ needle) = (l * D)/(\pi * D * l ) = (1)/(\pi )`

Therefore, the probability that the needle will cut the line = 1/π.