Answer
Options E, F and G are correct.
The last three options are all correct.
The correct options include:
- The probability that the selected student used a car or bus to get to school under the condition that the student is in high school is (321/333)
- The probability that the selected middle school or high school student used a car to get to school is (223/500)
- P(bus | middle school) > P(bus | high school)
Step-by-step explanation
To answer this, we will examine each of these options in the statement one at a time. Before that,
Probability of an event is calculated as the number of elements in that event divided by the total number of elements in the sample space.
Option A
The probability that the selected student used the bus to get to school under the condition that the student is in middle school is (260/500)
Number of middle school students that used the bus to get to school = 124
Total number of students in middle school = 167
The probability that the selected student used the bus to get to school under the condition that the student is in middle school = (124/167)
We can see that (124/167) ≠ (260/500)
So, option A is not correct.
Option B
The probability that the student is in middle school under the condition that the student takes the bus to school is (124/167)
Number of bus riders that are in middle school = 124
Total number of bus riders = 260
The probability that the student is in middle school under the condition that the student takes the bus to school is (124/260)
We can see that (124/260) ≠ (124/167)
So, option B is not correct.
Option C
P(car) = (38/500)
Number of car riders = 223
Total number of students = 500
P(car) = (223/500)
We can see that (223/500) ≠ (38/500)
So, option C is not correct.
Option D
The probability that the selected student used a car to get to school or is a middle student is (390/500)
Number of students that use a car to get to school or are middle schoolers = 38 + 185 + 124 + 5 = 352
Total number of students = 500
The probability that the selected student used a car to get to school or is a middle student = (352/500)
We can see that (352/500) ≠ (390/500)
So, option D is not correct.
Option E
The probability that the selected student used a car or bus to get to school under the condition that the student is in high school is (321/333)
Number of high school students that use a car or bus to get to school = 185 + 136 = 321
Total number of high school students = 333
The probability that the selected student used a car or bus to get to school under the condition that the student is in high school = (321/333)
We can see that (321/333) = (321/333)
So, option E is correct.
Option F
The probability that the selected middle school or high school student used a car to get to school is (223/500)
Number of middle or high school students that use a car to get to school = 38 + 185 = 223
Total number of middle or high school students = 167 + 333 = 500
The probability that the selected middle school or high school student used a car to get to school = (223/500)
We can see that (223/500) = (223/500)
So, option F is correct.
Option G
P(bus | middle school) > P(bus | high school)
P(A | B) means the probability of event A under the condition of event B.
P(bus | middle school) = Probability of a randomly selected student taking a bus to school under the condition that the student is in middle school.
Number of middle school students that used the bus to get to school = 124
Total number of students in middle school = 167
P(bus | middle school) = (124/167) = 0.743
P(bus | high school) = Probability of a randomly selected student taking a bus to school under the condition that the student is in high school.
Number of high school students that used the bus to get to school = 136
Total number of students in high school = 333
P(bus | middle school) = (136/333) = 0.408
0.743 > 0.408
(124/167) > (136/333)
P(bus | middle school) > P(bus | high school)
So, option G is correct too.
Hope this Helps!!!