Question - Calculating Probability of Point Location on a Line Segment
Solution:
The image shows a line segment AB that is divided into sections AC, CD, and DB with lengths 34, 44, and 61 respectively, which sum up to the total length of AB. To find the probability that a random point on AB will be on CD, we can use the following formula:\[ P = \frac{\text{Length of CD}}{\text{Total length of AB}} \]From the image, we know:Length of CD = 44Total length of AB = 34 (AC) + 44 (CD) + 61 (DB) = 139Now we can calculate the probability:\[ P = \frac{44}{139} \]To express this as a decimal rounded to the nearest hundredth, calculate 44 divided by 139, which gives approximately:\[ P \approx 0.3165 \]Rounded to the nearest hundredth:\[ P \approx 0.32 \]So, the probability that a random point on AB will be on CD is 0.32, rounded to the nearest hundredth.
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