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In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is :
  • a)
    2/3
  • b)
    1/6
  • c)
    1/3
  • d)
    5/6
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 o...
A →opted NCC
B →opted NSS
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Most Upvoted Answer
In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 o...
Given:
- Total number of students in the class = 60
- Number of students who opted for NCC = 40
- Number of students who opted for NSS = 30
- Number of students who opted for both NCC and NSS = 20

To find:
- Probability that the selected student has opted neither for NCC nor for NSS

Solution:
Step 1: Find the number of students who opted for either NCC or NSS.
- Number of students who opted for NCC or NSS = Number of students who opted for NCC + Number of students who opted for NSS - Number of students who opted for both NCC and NSS
- Number of students who opted for NCC or NSS = 40 + 30 - 20 = 50

Step 2: Find the number of students who opted for neither NCC nor NSS.
- Number of students who opted for neither NCC nor NSS = Total number of students - Number of students who opted for either NCC or NSS
- Number of students who opted for neither NCC nor NSS = 60 - 50 = 10

Step 3: Find the probability that the selected student has opted neither for NCC nor for NSS.
- Probability = Number of students who opted for neither NCC nor NSS / Total number of students
- Probability = 10 / 60 = 1/6

Therefore, the probability that the selected student has opted neither for NCC nor for NSS is 1/6. Hence, option B is the correct answer.
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In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is :a)2/3b)1/6c)1/3d)5/6Correct answer is option 'B'. Can you explain this answer?
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