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A point is chosen at random on the number line between $0$ and $1$, and the point is colored green. Then, another point is chosen at random on the number line between $0$ and $1$, and this point is colored purple. What is the probability that the number of the purple point is greater than the number of the green point, but less than twice the number of the green point

Respuesta :

The probability that the number of the purple point is greater than the number of the green point, but less than twice the number of the green point is 1/4

How to find the Probability?

Let the "green" value be an x value lying on segment AC.

Now, the segment AC has the equation y = x. Then, let the "purple" value that is twice a selected x value lie on the segment AE and as such, the equation of this line is y = 2x.

It must be noted that at point E, x = 0.5 and y = 1. This means at every x value on AC greater than 0.5, the value of y on EC associated with this x value is is less than twice that x value.

Then, between segments AE and AC, every value of y will be greater than, but less than twice, its associated x value.

Since triangle ACD has an area of 1/2 and triangle BEA has an area of 1/4, then we can say that;

Triangle AEC area = 1 - (1/2) - (1/4)   = 1/4.  

Thus,  the probability that the number of the purple point is greater than the number of the green point, but less than twice the number of the green point is 1/4

Read more about Probability at; https://brainly.com/question/251701

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