<p>If two points are selected at random from the interval [0,1], what is the probability that the distance between them is less than one-fourth?</p>
<p>OctalC0de had posted a nice, intuitive solution approach to a whole bunch of problems of this sort.</p>
<p>Let [0,1] on the x-axis represent all possible choices for point<em>1, and [0,1] on the y-axis represent all choices for point</em>2. Then draw the square (0,0) (0,1) (1,1) (1,0) ; this represents all possible combinations of values for both points.</p>
<p>Now draw 2 lines y = x + 0.25 and y = x - 0.25, and shade the area between them that's also within the square. The shaded area / (area of square) = probability that y is within x +/- 0.25 i.e. the probability you desire.</p>
<p>Shaded area = Area of square - area of triangle1 - area of triangle2
= (1)(1) - (0.5)(.75)(.75)- (0.5)(.75)(.75)
= 1 - (9/16)
= 7/16
Shaded area / area of square = (7/16) / 1 = 7/16 .</p>
<p>would this be an SATI math test question or II?</p>
<p>If it's on the SATs at all i think II? Wow I'm just happy I didn't get that problem when I took the SATs.</p>