Thread: finite probability question

A point X is chosen at random on a line sement AB. (a)show that the probability that the ratio of lengths AX/BX is smaller than a is = to a/(1+a). and (b) show that the probability that the ration of the length of the shorter segment to that of the longer is less than 1/3 is = to 1/2.

Originally Posted by lauren2988

A point X is chosen at random on a line sement AB. (a)show that the probability that the ratio of lengths AX/BX is smaller than a is = to a/(1+a). and (b) show that the probability that the ration of the length of the shorter segment to that of the longer is less than 1/3 is = to 1/2.

You may as well assume that the line segment is of length , and that you choose a point . Now the first part of the question becomes:

find give .

You do this by rearranging the condition into the form where is an expression in only.

CB

Originally Posted by lauren2988

A point X is chosen at random on a line sement AB. (a)show that the probability that the ratio of lengths AX/BX is smaller than a is = to a/(1+a). and (b) show that the probability that the ration of the length of the shorter segment to that of the longer is less than 1/3 is = to 1/2.

To do the second part we are being asked (same notation as before) to compute the probability that or

CB