Stat

Translate the following events into set notation using the symbols A and B, complement, union, intersection. Also give the probability of the event as determined from the table above. Fill in the table below with these values. {If you cannot construct the symbol ∩, just use & or copy and paste} Lastly, draw a Venn diagram (on scratch paper, but you need not submit it) showing the events of Female, Public, and both Female and Public. The first one is completed for you.

Event in words Event in set notation Probability
Female and Public A ∩ B P(A ∩ B) = 0.38
Female and Private
Public and Male

Neither Female nor Public

c. Determine the probability that the student is Male. Do the same for student attending a Private high school. Use proper event notation remember that A is Female and B is Public.
A ∩ B
.
d. If you had not been given the table, but instead had merely been told that P(A)=.45 and P(B)=.84, would you have been able to calculate P(Ac) and P(Bc)? Explain how.

e. Calculate the probability that at least either the student is Female or the student attended a Public high school.

f. Another way to calculate P(A ∪ B) in part e is to use the complement of the event. First, in words what is the complement to the event described in e and then find this probability using the complement. Does this match your answer in e?

g. If you had not been given the table but instead had merely been told P(A)=.45 and P(B)=.84 and were asked to calculate P(A ∪ B), you might first consider P(A)+P(B). Calculate this sum and compare the result to your answer for e. Are they the same? Is this even a legitimate answer?

h. Given the knowledge that the student is Female, what is the conditional probability that the student attended a Public high school? [Hint: Restrict your consideration to Females, and ask yourself what fraction of those female students attended a Public high school?]

i. How does this conditional probability of the student attending a Public high school given that the student is Female compare with the unconditional probability of the student attending a Public high school? Does the knowledge that the student is Female make it more or less likely (or neither) that the student attended a Public high school?

  1. 👍 0
  2. 👎 0
  3. 👁 394
  1. this is the chart for this problem
    Public Private Total
    Female 38 7 45
    Male 46 9 55
    Total 84 16 100

    1. 👍 0
    2. 👎 0
  2. P(B|A) = (P(A and B))/(P(A)) = (.38)/(.45) = 0.84

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    Consider the set of integers greater than -2 and less than 6. A subset of this set is the positive factors of 5. What is the complement of this subset? a. {0,2,3,4} b. {-1,0,2,3,4} c. {-2,-1,0,2,3,4,6} d. {-2,-1,0,1,2,3,4,5,6} I

    asked by Angie on May 25, 2009
  2. math

    Find the measure of the complement and the supplement of an angle with a measure of 20 degrees? complement, 150; supplement, 260 complement, 340; supplement, 160 *complement, 70; supplement, 160* complement, 160; supplement, 70

    asked by blah on April 4, 2017
  3. Finite Math

    Let A and B be two events in a sample space S such that P(A) = 0.5, P(B) = 0.6, and P(A intersection B) = 0.15. Find the probabilities below. Hint: (A intersection Bc) union (A intersection B) = A. (a) P(A|Bc) ________ (b) P(B|Ac)

    asked by Seth on November 20, 2014
  4. Algebra 2

    Rewrite each set in the indicated notation. 1. {-9, -7, -5, -3, -1}; set-builder notation. A: ?

    asked by Victoria on September 2, 2014
  5. Math

    Express each set in set-builder notation: Set D is the set of natural numbers between 27 and 51, inclusive.

    asked by Jen on July 5, 2011
  1. MATH

    I need help idk how to do this... Select the measure of the complement or supplement of the angle. If there is no complement or supplement, select no complement or supplement. 55.1° (1 point) 124.9° 119.9° 49.9° no complement

    asked by Gabby on February 2, 2013
  2. Algebra

    Algebra Help? Union & Intersection of Sets, Complement and Cross Product, Relations &Functions,Venn Diagram? I did a survey on which type of pie they like I already drew the vinn diagram but cant Jiskha does not accept that

    asked by TiffanyM on November 18, 2010
  3. math/algebra

    Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation x^3+x^2+16x+16>0 What is the solution set? (Type your answer in interval notation.) shannon

    asked by shannon on February 5, 2016
  4. math

    Determine the intersection X ∩ Y. Express the in interval notation. X = {x } and Y = {x

    asked by Barb on February 15, 2019
  5. Math

    Select the measure of the complement or supplement of the angle. If there is no complement or supplement, select no complement or supplement. 55.1° (1 point) 124.9° 119.9° 49.9° no complement or supplement

    asked by Mothy on January 27, 2014
  6. Math

    Using set notation (union, intersection, complement,etc.) write the following subset in terms of T,V,S: the set of potters selling vases and tableware, but not sculptures. My answer: (VintersectT) intersect S complement

    asked by Lijim on December 8, 2019

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