The frequency table below shows the number of freshmen and sophomores in a Geometry class that passed or failed the final exam.
Freshman: Pass 137; Fail=8
Sophomore:Pass 111; Fail=13
If a student is chosen at random, which of the following probabilities are true? Select ALL that apply. Probabilities are rounded to the nearest hundredth.

A. The probability that the student failed given that they are a freshman is 0.62.
B. The probability that the student is a sophomore given that they pass is 0.90.
C. The probability that the student passed given that they are a sophomore is 0.90.
D. The probability that the student is a freshman given that they failed is 0.38.
E. The probability that the student is a sophomore given that they failed is 0.10.
F. The probability that the student passed given that they are a freshman is 0.94.

A would not be correct since given they are a freshman and the probability of them failing would be 0.06 or 6% since the fraction is 8 out 145. 8 out of 145 equates to 6% or 0.06 when rounded to the nearest hundredth.

B is correct since the probability that a student is a sophomore given that they pass is 0.90 if rounded to the nearest hundredth. This would be correct since 111 out of 124 is 0.895, then we round it to the nearest hundredth, that means it is 0.90 probability or 90% that a sophomore passes.

C is correct since it is the same as B but just reworded to the context in which what the probability is for a student to pass given that they are a sophomore.

D would not be correct as it is also worded different but is the same as A. The probability of a student who is a freshman given that they failed is 0.06 or 6%, so D isn't correct.

E would be correct depending on the way we round it since, 13 out of 124 is .1048, if we didn't round the ten thousandths place to the thousandths and then we can raise the hundreds place to 1. In this case, I would say it is correct since it is very close to 10% or .10

F would be correct since the probability of a freshman failing is 0.06 and all we need to do to find the passing probability is subtract 0.06 from 1.

1 - 0.06 = 0.94.  Thus the probability that the student passed given that they are a freshman is 0.94 or 94%.

Correct Answers List: B, C, E, and F.

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