out of 250 students interviewed at a community college, 90 were taking mathematics but not computer science, 160 were taking mathematics, and 50 were taking neither mathematics nor computer science. Find the probability that a student chosen at random was
a. taking just computer science
b. taking mathematics or computer science, but not both
c. taking computer science
d. not taking mathematics
e. taking mathematics, given that the student was taking computer science
f. taking computer science, given that the student was taking mathematics
g. taking mathematics, given that the student was taking computer science or mathematics
h. taking computer science, given that the student was not taking mathematics
i. not taking mathematics, given that the student was not taking computer science
It would help if you proofread your questions before you posted them. You have not indicated that anybody is taking computer science or both.
This is exactly how the question is written on the test. Does that mean it can't be answered since we don't have part of the problem?
it's possible. You know 160 are taking math and OF the 160 90 are ONLY taking math leaving 70 taking both. 90+70(160) + 50 = 210. so 40 are taking c.s. but not math
90-math
70-math & c.s.
40-c.s.
50-neither
the rest is a:40/250, b:(90+40)/250, C:40/250, d:(50+40)/250
e gets tricky now is probability of students taking math out of the pool of (70+40)(the number taking c.s.) so 70/110
etc. etc.
To find the probability for each scenario, we need to calculate the number of students in each category and then divide by the total number of students (250). Let's go through each scenario one by one:
a. Taking just computer science:
This refers to the number of students taking computer science but not mathematics. According to the given information, 90 students are taking mathematics but not computer science. Therefore, the probability is 90/250.
b. Taking mathematics or computer science, but not both:
This refers to the number of students taking either mathematics or computer science, but not both. To find this, we need to subtract the number of students taking both mathematics and computer science from the total number of students taking either subject. According to the given information, 160 students are taking mathematics and 90 students are taking mathematics but not computer science. So, the number of students taking both subjects is 160 - 90 = 70. Therefore, the probability is (90 + 70)/250.
c. Taking computer science:
This refers to the number of students taking computer science. According to the given information, 90 students are taking computer science but not mathematics, and 70 students are taking both subjects. So, the number of students taking computer science is 90 + 70 = 160. Therefore, the probability is 160/250.
d. Not taking mathematics:
This refers to the number of students not taking mathematics. According to the given information, 50 students are taking neither mathematics nor computer science. So, the probability is 50/250.
e. Taking mathematics, given that the student was taking computer science:
This refers to the number of students taking both mathematics and computer science, given that they are taking computer science. According to the given information, 70 students are taking both subjects, and 160 students are taking computer science. So, the probability is 70/160.
f. Taking computer science, given that the student was taking mathematics:
This refers to the number of students taking both subjects, given that they are taking mathematics. According to the given information, 70 students are taking both subjects, and 160 students are taking mathematics. So, the probability is 70/160.
g. Taking mathematics, given that the student was taking computer science or mathematics:
This refers to the number of students taking mathematics, given that they are taking either mathematics or computer science. According to the given information, 70 students are taking both subjects, 90 students are taking mathematics but not computer science, and 160 students are taking computer science. So, the probability is (70 + 90 + 160)/250.
h. Taking computer science, given that the student was not taking mathematics:
This refers to the number of students taking computer science, given that they are not taking mathematics. According to the given information, 90 students are taking mathematics but not computer science, and 50 students are taking neither subject. So, the probability is 50/(90 + 50).
i. Not taking mathematics, given that the student was not taking computer science:
This refers to the number of students not taking mathematics, given that they are not taking computer science. According to the given information, 50 students are taking neither subject. So, the probability is 50/250.
By using the given information and following the steps outlined for each scenario, you can compute the precise probability for each case.