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A Science test and an English test were administered to a class of 30 students. Half of the students passed in Science, 60% of the students passed in English and 10% failed in both. If a student is selected at random from the class, what is the probability that the student has passed in at least one of the two tests?
- a)1/10
- b)1/5
- c)3/4
- d)4/5
- e)9/10
Correct answer is option 'E'. Can you explain this answer?
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A Science test and an English test were administered to a class of 30 ...
Step I: Define Non-event
1 student is selected at random out of a class of 30 students. The event in this question is that the selected student has passed in at least one of the two tests.
Since a majority of the students have passed at least one of the two sets (it is given that only 10% of the students have failed in both tests), the number of ways in which the event can occur will be far more than the number of ways in which the non-event can occur.
So, this question will be solved more quickly through the non-event method.
The non-event in this case will be that the selected student has failed in both the tests.
So, the probability event equation is:
P(Student has passed at least 1 test) = 1 – P(Student has failed both tests)
Step II: Find n, the number of ways in which all outcomes can occur
Now, the total number of ways in which 1 student can be selected out of 30 students
= 30C1 = 30
So, n = 30
Step III: Find x, the number of ways in which the Non-event can occur
The non-event is the selection of a student who has failed both tests.
From the question statement, we know that
Number of students who failed both tests = 10% of all students
= 10% of 30 = 3
Thus, the non-event occur if one of out of these 3 students is selected.
Number of ways in which this can happen = 3C1 = 3
So, x = 3
Step IV: Calculate probability for Non-event
P(Student has failed both tests)
Step V: Probability (Event) = 1-Probability (Non-event)
Now, let’s put the value of P (Non-event) in the probability event equation:
P(Student has passed at least 1 test) = 1 – P(Student has failed both tests)
Step V: Probability (Event) = 1-Probability (Non-event)
Now, let’s put the value of P (Non-event) in the probability event equation:
P(Student has passed at least 1 test) = 1 – P(Student has failed both tests)
Answer: Option (E)
Most Upvoted Answer
A Science test and an English test were administered to a class of 30 ...
To solve this problem, we need to use the concept of probability. Let's break down the information given and solve the problem step by step.
Given information:
- There are 30 students in the class.
- Half of the students passed in Science, which means 50% of the students passed the Science test.
- 60% of the students passed in English.
- 10% of the students failed in both Science and English.
Step 1: Determine the number of students who passed the Science test.
Since half of the students passed the Science test, we can calculate the number of students who passed as follows:
Number of students passed in Science = (50/100) * 30 = 15
Step 2: Determine the number of students who passed the English test.
Since 60% of the students passed the English test, we can calculate the number of students who passed as follows:
Number of students passed in English = (60/100) * 30 = 18
Step 3: Determine the number of students who failed in both Science and English.
Since 10% of the students failed in both Science and English, we can calculate the number of students who failed in both as follows:
Number of students failed in both = (10/100) * 30 = 3
Step 4: Determine the number of students who passed at least one of the tests.
To find the number of students who passed at least one of the tests, we need to subtract the number of students who failed in both from the total number of students:
Number of students passed at least one test = 30 - 3 = 27
Step 5: Calculate the probability of a student passing at least one of the tests.
The probability of a student passing at least one of the tests is the number of students who passed at least one test divided by the total number of students:
Probability = Number of students passed at least one test / Total number of students
Probability = 27 / 30 = 9/10
Therefore, the probability that a student selected at random from the class has passed at least one of the two tests is 9/10.
Given information:
- There are 30 students in the class.
- Half of the students passed in Science, which means 50% of the students passed the Science test.
- 60% of the students passed in English.
- 10% of the students failed in both Science and English.
Step 1: Determine the number of students who passed the Science test.
Since half of the students passed the Science test, we can calculate the number of students who passed as follows:
Number of students passed in Science = (50/100) * 30 = 15
Step 2: Determine the number of students who passed the English test.
Since 60% of the students passed the English test, we can calculate the number of students who passed as follows:
Number of students passed in English = (60/100) * 30 = 18
Step 3: Determine the number of students who failed in both Science and English.
Since 10% of the students failed in both Science and English, we can calculate the number of students who failed in both as follows:
Number of students failed in both = (10/100) * 30 = 3
Step 4: Determine the number of students who passed at least one of the tests.
To find the number of students who passed at least one of the tests, we need to subtract the number of students who failed in both from the total number of students:
Number of students passed at least one test = 30 - 3 = 27
Step 5: Calculate the probability of a student passing at least one of the tests.
The probability of a student passing at least one of the tests is the number of students who passed at least one test divided by the total number of students:
Probability = Number of students passed at least one test / Total number of students
Probability = 27 / 30 = 9/10
Therefore, the probability that a student selected at random from the class has passed at least one of the two tests is 9/10.
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A Science test and an English test were administered to a class of 30 students. Half of the students passed in Science, 60% of the students passed in English and 10% failed in both. If a student is selected at random from the class, what is the probability that the student has passed in at least one of the two tests?a)1/10b)1/5c)3/4d)4/5e)9/10Correct answer is option 'E'. Can you explain this answer?
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A Science test and an English test were administered to a class of 30 students. Half of the students passed in Science, 60% of the students passed in English and 10% failed in both. If a student is selected at random from the class, what is the probability that the student has passed in at least one of the two tests?a)1/10b)1/5c)3/4d)4/5e)9/10Correct answer is option 'E'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A Science test and an English test were administered to a class of 30 students. Half of the students passed in Science, 60% of the students passed in English and 10% failed in both. If a student is selected at random from the class, what is the probability that the student has passed in at least one of the two tests?a)1/10b)1/5c)3/4d)4/5e)9/10Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Science test and an English test were administered to a class of 30 students. Half of the students passed in Science, 60% of the students passed in English and 10% failed in both. If a student is selected at random from the class, what is the probability that the student has passed in at least one of the two tests?a)1/10b)1/5c)3/4d)4/5e)9/10Correct answer is option 'E'. Can you explain this answer?.
A Science test and an English test were administered to a class of 30 students. Half of the students passed in Science, 60% of the students passed in English and 10% failed in both. If a student is selected at random from the class, what is the probability that the student has passed in at least one of the two tests?a)1/10b)1/5c)3/4d)4/5e)9/10Correct answer is option 'E'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A Science test and an English test were administered to a class of 30 students. Half of the students passed in Science, 60% of the students passed in English and 10% failed in both. If a student is selected at random from the class, what is the probability that the student has passed in at least one of the two tests?a)1/10b)1/5c)3/4d)4/5e)9/10Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Science test and an English test were administered to a class of 30 students. Half of the students passed in Science, 60% of the students passed in English and 10% failed in both. If a student is selected at random from the class, what is the probability that the student has passed in at least one of the two tests?a)1/10b)1/5c)3/4d)4/5e)9/10Correct answer is option 'E'. Can you explain this answer?.
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