Need help with probability (theory and calculation)

Feb 2009
155
1
Hi all

Greetings. Need help to check & help with the questions below:

Gender\MajorAccountingManagementEconomicsTotal
Male
8012030230
Female506020130
Total13018050360

(a) Give an example of a simple event. --- Need help
(b) Give an example of a joint event. --- Need help

(c) Compute the probability of choosing Management or Economics.
(180/360 + 50/360) = 23/36

(d) Compute the probability of choosing a male and Management major.
(230/360)*(180/360) = 23/72

(e) Given that the person selected is female, compute the probability ofchoosing an Accounting major.
50/360 = 5/36

(f) Are “gender” and “major” independent? Explain. --- Need help


All help appreciated, thank you in advance.
 

romsek

MHF Helper
Nov 2013
6,828
3,073
California
A simple event would be one that only involves random variable such as "a male majors in ____"

A joint even would be one with multiple random variables such as "a male majors in ____ and a female majors in ____

(c) happens to be correct but by luck. P(A or B) = P(A) + P(B) - P(A and B). A better way of computing this would be to note that there are 230 people who majored in either Management or Economics out of 360 total. Note that P(A and B)=0 as one can only major in a single field.

(d) is incorrect. P(AB)=P(A)P(B) only if A and B are independent events. There are 120 male management majors out of 360 people so the probability is $\dfrac{120}{360}=\dfrac 1 3$

(e) is incorrect. You are given the student is female so P(acct | female) = 50/130 = 5/13

(f) there are a few ways to show that they are not independent. A simple way is to note P[acct and male] = 80/360, P[acct]=130/360, P[male]=230/360, P[acct][male]=(130x230)/(360x360)=299/1296 which is not equal to 80/360.
 
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