If three straight lines are drawn on a white board at random with the eyes closed, show that the probability of forming a triangle is 1/7.
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Answers
Answer:
Probability of formation of triangle = 1/7
Step-by-step explanation:
If we draw three lines randomly on white paper then there only 7 possibilities in which lines can be drawn.
All possibilities are following
1): All lines coincide means all three lines properly covered each other and looks like one line.
2): Two out of three coincide and one line parallel to them means two lines properly covered each other to looks like one line and third one parallel to them.
3): All lines are parallel to each other and do not covered each other.
4): All lines intersect at three distinct(not same) points
5): Two out of three lines parallel each other and third one intersect them like a transversal line.
6): Two lines coincide means two lines properly covered each other to look like a one line and third one intersect them.
7): All lines pass through a common point that is all lines insect at single point
In the number 4 point the lines formed the triangle so out of 7 there is only possibility to formed the triangle.
Total sample space = 7
Desire space = 1
Probability = desire space / sample space
Putting the values we get
Probability of formation of triangle = 1/7