Question The table below shows a probability density function for a discrete random variable X, the number of times high school
students study in the school library per week. What is the probability that X is 2?
• Provide the final answer as a fraction.
Х
0
-
P(X = x)
1/3
1/12
1/12
1
2.
3
1/3
1/6
4
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geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

the solution, from the graphing of the two lines, is (3,2), i.e., x = 3, y = 2.