Question

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

Answer 1

Tell me why the answer I got are wrong please

Answer 2

@dan815

Answer 3

can you tell us how you tried to solve this problem?

Answer 4

using a tree but it obviously did not work

Answer 5

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

Answer 6

I did that

Answer 7

I did (.55*.55)+(.05*.4)+(.25*.2)+(.2*.2)

Answer 8

Is it wrong?

Answer 9

wait i think i see my mistake

Answer 10

wait I have no clue what I did

Answer 11

\[P(m) = P(m\cap s) + P(m \cap j) +\cdots\\ = P(m|s)P(s) + P(m|j)P(j)+ \cdots\]

so i think its same as what youve done the answer should be correct.. does it give a correct answer?

Answer 12

yeah when I get the correct answer but it isn't

Answer 13

what does it state as the correct answer?

Answer 14

It doesn't. It will only say if its correct when I get the correct answer

Answer 15

I think your answer is correct :(

Answer 16

@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.

Answer 17

why (.15*.2)

Answer 18

@dan815

Answer 19

its the correct answer but why?

Answer 20

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.

Answer 21

oh! that makes sense now :D

Answer 22

This is the same way that you have correctly calculated the values of the other three intersections.

Answer 23

oh okay

Answer 24

You're welcome :)

Answer 25

thank you