Assume that the class consists of 55 percent freshmen, 5 percent sophomores, 25 percent juniors, and 15 percent seniors. Assume further that 55 percent of the freshmen, 40 percent of the sophomores, 20 percent of the juniors, and 20 percent of the seniors plan to go to medical school. One student is selected at random from the class. (1) What is the probability that the student plans to go to medical school? .4125 (2) If the student plans to go to medical school, what is the probability that he is a sophomore? .02/.4125

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Assume that the class consists of 55 percent freshmen, 5 percent sophomores, 25 percent juniors, and 15 percent seniors. Assume further that 55 percent of the freshmen, 40 percent of the sophomores, 20 percent of the juniors, and 20 percent of the seniors plan to go to medical school. One student is selected at random from the class. (1) What is the probability that the student plans to go to medical school? .4125 (2) If the student plans to go to medical school, what is the probability that he is a sophomore? .02/.4125

Mathematics
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Tell me why the answer I got are wrong please
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Other answers:

using a tree but it obviously did not work
first try to write the given information in a notatio.. freshman = f junior = j sophomore = so senior = s the following are given,\[P(f), P(s), P(so), P(j)\] And also if selecting medicine is m \[P(m|j) = 0.2, P(m|s) = 0.2\] The question asks for probability of the selected student hopes to do medicine -> P(m) use the conditional probability equations to obtain that
I did that
I did (.55*.55)+(.05*.4)+(.25*.2)+(.2*.2)
Is it wrong?
wait i think i see my mistake
wait I have no clue what I did
\[P(m) = P(m\cap s) + P(m \cap j) +\cdots\\ = P(m|s)P(s) + P(m|j)P(j)+ \cdots\] so i think its same as what youve done the answer should be correct.. does it give a correct answer?
yeah when I get the correct answer but it isn't
what does it state as the correct answer?
It doesn't. It will only say if its correct when I get the correct answer
I think your answer is correct :(
@Pulsified333 "I did (.55*.55)+(.05*.4)+(.25*.2)+(.2*.2)" The last term in brackets should be .......+(.15 * .2). With this correction the sum of the terms is 0.4025 which is the probability that the student plans to go to medical school.
why (.15*.2)
its the correct answer but why?
The question states that 15% of the class is seniors, and 20% of the seniors plan to go to medical school. The intersection of P(senior) and P(med.school|senior) = .15 * .2.
oh! that makes sense now :D
This is the same way that you have correctly calculated the values of the other three intersections.
oh okay
You're welcome :)
thank you

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