Students at Warlock High are allowed to sign up for one social studies class each year. The numbers in each grade level signing up for various classes for the next school year are given in the following table:

Grade US History Civics World History Economics Total
10th 75 10 125 5 215
11th 130 85 75 60 350
12th 35 150 50 105 340
Total 240 245 250 170 905

Part A: What is the probability that a student will take Civics? (2 points)

Part B: What is the probability that a 10th-grader will take either US History or World History? (2 points)

Part C: What is the probability that a student will take Economics given that he or she is in the 10th grade? (2 points)

Part D: Consider the events "A student takes Civics" and "A student is a 12th-grader." Are these events independent? Justify your answer. (4 points)

part b: students of 10th grade taking history/ total students+ students of 10th grade taking world history/total students= 75/905 + 125/905=200/905= 0.221

part c: number of students taking economics/total students of 10th grade= 5/215=0.0233

part d: This is not independent because there is a intersection of 12th grade and civics subjects we can use a formula also, if they are independent we can write

P(civics/12th)=P(civics)

we have

150/340 ( not equal to) 245/905

they are dependent

MrRoyal MrRoyal · Answer 2 · 2021-12-30T16:51:55+01:00

Probabilities are used to calculate the chances of the outcomes of events.

(a) The probability that a student will take Civics

From the table, we have:

[tex]Civics = 245[/tex] --- students that take civics

[tex]Total = 905[/tex] --- the total number of students

So, the probability is:

[tex]Pr = \frac{245}{905}[/tex]

[tex]Pr = 0.2707[/tex]

Hence, the probability that a student will take Civics is 0.2707

(a) The probability that a 10th-grader will take either US History or World History

From the table, we have:

[tex]US\ History + World\ History = 75 + 125 = 200[/tex] --- 10th graders that take US History or World History

[tex]Total = 215[/tex] --- the total number of 10th graders

So, the probability is:

[tex]Pr = \frac{200}{215}[/tex]

[tex]Pr = 0.9302[/tex]

Hence, the probability that a 10th-grader will take either US History or World History is 0.9302

(c) The probability that a student will take Economics given that he or she is in the 10th grade

From the table, we have:

[tex]Economics = 5[/tex] --- 10th graders that take Economics

[tex]Total = 215[/tex] --- the total number of 10th graders

So, the probability is:

[tex]Pr = \frac{5}{215}[/tex]

[tex]Pr = 0.0233[/tex]

Hence, the probability that a student will take Economics given that he or she is in the 10th grade is 0.0233

(d) Independent events

For two events A and B to be independent, then the following must be true

P(A and B) = 0

However, P(A and B) [tex]\ne[/tex] 0, for events "A student takes Civics" and "A student is a 12th-grader."

This is so because, 12th grader students take Civics.

Hence, the events are not independent