Probability

At a certain university, 30% of the students major in math. Of the students majoring in math, 60% are males. Of all the students at the university, 70% are males.
a) What is the probability that a student selected at random in the university is male and majors in math?

b) What is the probability that a randomly selected student in the university is female or majors in math or both?

Based upon the information you provided, out of every 100 students you have this breakdown:
male, math major: 18
female, math major: 12
male, non-math major: 52
female, non-math major: 18

therefore:
a) 18%
b) female: 30%
math major (either sex): 30%
female math major: 12%

so for b), you just add them up to get 72%?

  1. 👍 0
  2. 👎 0
  3. 👁 845
  1. this probably wrong, see correct answer below
    P(Math) = 0.30
    P(Male | Math) = 0.60
    P(Male) = 0.70

    P(Male ∩ Math) = P(Male | Math) ⋅ P(Math) = 0.60 ⋅ 0.30 = 0.18

    P(Female) = P(¬Male) = 1 − P(Male) = 1 − 0.70 = 0.30
    P(Math) = 0.30
    P(Female | Math) = P(¬Male | Math) = 1 − P(Male | Math) = 1 − 0.60 = 0.40
    P(Female ∩ Math) = P(Math) ⋅ P(Female | Math) = 0.30 ⋅ 0.40 = 0.12

    P(Female ∪ Math) = P(Female) + P(Math) − P(Female ∩ Math) = 0.30 + 0.30 − 0.12 = 0.48

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. stats

    Which of the following variables for data about a track team is a discrete variable? C?? The height of a team member A The weight of a team member B The number of times that a team member finished first in a race C The time

  2. statistics

    The GPAs of all students enrolled at a large university have an approximately normal distribution with a mean of 3.02 and a standard deviation of .29. Find the probability that the mean GPA of a random sample of 20 students

  3. Statistics

    A survey of undergraduate students in the School of Business at Northern University revealed the following regarding the gender and majors of the students: Major Gender Accounting Management Finance Total Male 100 150 50 300

  4. English

    Choose the sentence that is written in active voice. A. The math problems were given to the students. B. The students were taking a math test. C. The math test was given by the instructor. D. The math test grades were given to the

  1. Economics

    Suppose a university decides to alter its tuition schedule by separating its students based on how many years of college they have completed. Most university programs require four years to complete. First-year students would get a

  2. Business English

    Choose the sentence that is written in active voice. a) The math problems were given to the students. b) The students were taking a math test. c) The math test was given by the instructor. d) The math test grades were given to the

  3. Math

    I have a bar graph that shows the number of students by major in the College of Arts and Science. Math shows 200 students History shows 300 students English shows 400 students Science shows 150 students Other shows 175 students

  4. Math

    What percent of students in the college are history majors (to the nearest tenth of a percent)? 200 students major in math 300 students major in history 400 major in english 150 major in science 175 major in other Total number of

  1. probability

    University students average 7.2 hours of sleep per night with a standard deviation of 40 minutes. If the amount of sleep is normally distributed, what proportion of university students sleep for more than 8 hours

  2. Statistics

    The proportion of students who own a cell phone on college campuses across the country has increased tremendously over the past few years. It is estimated that approximately 90% of students now own a cell phone and 10% do not own

  3. Math

    A university conducts a study of tobacco use among 1000 of its students. Researchers survey male volunteers and female volunteers to find the frequency of tobacco use. The study finds that, of the people surveyed, 250 men and 50

  4. Math

    A state university wants to increase its retention rate of 4% for graduating students from the previous year. After implementing several new programs during the last two years, the university reevaluated its retention rate.

You can view more similar questions or ask a new question.