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I need help finding the probability from the following data given in a table.

Question: A survey of students in a large Introductory Statistics class asked about their birth order (1 = “oldest or only child”; 2 = others) and which faculty of the university they were studying under. Here are the data:

 Faculty            Birth Order     Birth Order     Total
                        1                2

 Arts and Sciences      34              23
 Agriculture            52              41
 Human Ecology          15              28
 Other                  12              18
                       113              110         223
  1. Is we select a student at random, what is the probability that the person is an Arts and Sciences student who is not “oldest or only child”?
  2. Among the Arts and Sciences students, what is the probability that a student was the “oldest or only child”?
  3. What is the probability that an “oldest or only child” is enrolled in the Agriculture Faculty?
  4. What is the probability that a randomly selected student is either the “oldest or only child” or enrolled in the Faculty of Human Ecology?

What I think/tried:

  1. 23/223 = 0.103139013
  2. 34/57 = 0.596491228
  3. 52/113 = 0.460176991
  4. Need help with number 4.

Now I don't know if I am right or wrong. So can someone help me with number 4 and also tell me what i did was right and If i am wrong...can you also tell me what i did wrong and how i can solve it.

Thank you.

1 Answers 1

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Your answers for parts (1)-(3) are good. From the table, we observe that

   Total number of students who is the oldest or only child or enrolled in the Faculty of Human Ecology
= Number of students who is the oldest or only child + number of students who is the not "oldest or only child" enrolled in the Faculty of Human Ecology
= 113 + 28
= 141

Hence, the probability for part (4) is $\frac{141}{223}\approx 0.632287$.