Answer:
B. The probability of selecting an undergraduate and registered online student is 0.604
Step-by-step explanation:
Given
-----------------------Registered Online Registered In Person
Undergraduate --211 -- 347
Graduate --- 329 --- 581
Required
Probability that a randomly selected student is either an
undergraduate or registered online
First all data need to be properly represented..
Let U, G, Ro and Rp represented Undergraduate, Graduate, Registered online and Registered in person respectively
The data on first row represent data for undergraduate;.
Hence U = 211 + 347
U = 558
The data on the second row represent data for graduate;.
Hence G = 329 + 581
G = 910
The data on first column represent data for registered online
Hence Ro = 211 + 329
Ro = 540
The data on the second column represent data for registered in person;.
Hence Rp = 347 + 581
Rp = 928
Total student that participated in the survey = 211 + 347 + 329 + 581
Total = 1468
Probability that a randomly selected student is either an undergraduate or registered online is represented as P(U or Ro)
From probability formula;
P(U or Ro) is calculated as follows
P(U or Ro) = P(U) + P(Ro) - P(U and Ro)
Where P(U) = probability of selecting an undergraduate student
P(U) = number of undergraduates divided by total
[tex]P(U) = \frac{558}{1468}[/tex]
P(Ro) = probability of selecting a registered online student
P(Ro) = number of registered online student divided by total
[tex]P(Ro) = \frac{540}{1468}[/tex]
P(U and Ro) = probability of selecting an undergraduate and registered online student
P(U and Ro) = number of undergraduates and registered online students divided by total
From the table above, number of undergraduates and registered online = 211
[tex]P(U and Ro) = \frac{211}{1468}[/tex]
By substituting each of these expressions, we have
[tex]P(U or Ro) = \frac{558}{1468}+ \frac{540}{1468} - \frac{211}{1468}[/tex]
[tex]P(U or Ro) = \frac{558 + 540 - 211}{1468}[/tex]
[tex]P(U or Ro) = \frac{887}{1468}[/tex]
[tex]P(U or Ro) = 0.604223[/tex]
[tex]P(U or Ro) = 0.604[/tex] (Approximated).
Hence, probability of selecting an undergraduate and registered online student is 0.604
