Students at Praline High are allowed to sign up for one English class each year. The numbers of students signing up for various English
classes for the next school year are given in the following table:
Grade English English | English III English IV Total
10th
60
165
20
15
260
11th
35
40
115
10
200
12th
10
25
90
145
270
Total 105
230
225
170
730
Part A: What is the probability that a student will take English IV? (2 points)
Part B: What is the probability that an 11th-grader will take either English Il or English 111? (2 points)
Part C: What is the probability that a student will take English III given that he or she is in the 11th grade? (2 points)
Part D: Consider the events "A student takes English I" and "A student is a 10th-graderAre these events independent? Justify your answer.
(4 points) (10 points)

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anjelenamontalv anjelenamontalv · Answer 1 · 2020-10-21T19:19:53+02:00

Answer:

Part D: Yes, they're discussing grade level and a school subject. Unless they state the 10th grader is taking English I, it is independent.

Step-by-step explanation:

Since this was the only one they left out :)

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fichoh fichoh · Answer 2 · 2021-11-06T06:27:23+01:00

Using the concept of probability, the likelihood of the given events using the two-way table are :

From the two-way table :

P(English IV) = [tex] \frac{n(English IV)}{n(Total)} = \frac{170}{730} = 0.233 [/tex]

Part B :

P(11th grader takes English 11 or English 111)

[tex] \frac{n(English\:I1 + English \: 111)}{n(11th \: grader)} = \frac{(40+115)}{200} = 0.775 [/tex]

Part C:

P(English 3 | 11th grade) = [tex] \frac{n(English\: 111 \: n 11th grade)}{n(11th \: grade)} = \frac{115}{200} = 0.575 [/tex]

Part D :

Let :

The events are independent if :

P(AnB) = [tex] \frac{60}{730} = 0.082 [/tex]

P(A) × P(B) = [tex] \frac{105}{730} \times \frac{260}{730} = 0.0512 [/tex]

Hence, (AnB) ≠ p(A) × p(B)

Therefore, the events are not independent.

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