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In a shelf, there are 7 Banking awareness, 6 English and 5 GK books. One book is picked up randomly. What is the probability that it is neither in Banking awareness nor in GK ?
- a)1/13
- b)2/17
- c)1/3
- d)12/27
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
In a shelf, there are 7 Banking awareness, 6 English and 5 GK books. O...
P = 6/18 = 1/3
Most Upvoted Answer
In a shelf, there are 7 Banking awareness, 6 English and 5 GK books. O...
From the question we have to select only english book so 6 english books and total number of books =18
6/18=1/3
6/18=1/3
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In a shelf, there are 7 Banking awareness, 6 English and 5 GK books. O...
Question: In a shelf, there are 7 Banking awareness, 6 English and 5 GK books. One book is picked up randomly. What is the probability that it is neither in Banking awareness nor in GK?
Solution:
Total number of books in the shelf = 7 + 6 + 5 = 18
Let A be the event that the book picked up is from Banking awareness and B be the event that the book picked up is from GK.
We need to find the probability that the book picked up is neither in Banking awareness nor in GK, which can be represented as A' ∩ B', where A' represents the event that the book is not from Banking awareness and B' represents the event that the book is not from GK.
Now, we can find the probabilities of A and B using the formula:
P(A) = Number of books in Banking awareness shelf / Total number of books in the shelf
= 7/18
P(B) = Number of books in GK shelf / Total number of books in the shelf
= 5/18
Using the formula for finding the probability of intersection of two events, we can find the probability of A' ∩ B' as:
P(A' ∩ B') = 1 - P(A ∪ B)
where P(A ∪ B) represents the probability of the book picked up being either from Banking awareness or from GK or both.
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
where P(A ∩ B) represents the probability of the book picked up being both from Banking awareness and from GK.
We can find P(A ∩ B) as:
P(A ∩ B) = Number of books that are both in Banking awareness and GK shelf / Total number of books in the shelf
= 0 (since there are no books that are both in Banking awareness and GK shelf)
Substituting the values, we get:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
= 7/18 + 5/18 - 0
= 12/18
= 2/3
Therefore, P(A' ∩ B') = 1 - P(A ∪ B)
= 1 - 2/3
= 1/3
Hence, the probability that the book picked up is neither in Banking awareness nor in GK is 1/3.
Therefore, the correct answer is option C) 1/3.
Solution:
Total number of books in the shelf = 7 + 6 + 5 = 18
Let A be the event that the book picked up is from Banking awareness and B be the event that the book picked up is from GK.
We need to find the probability that the book picked up is neither in Banking awareness nor in GK, which can be represented as A' ∩ B', where A' represents the event that the book is not from Banking awareness and B' represents the event that the book is not from GK.
Now, we can find the probabilities of A and B using the formula:
P(A) = Number of books in Banking awareness shelf / Total number of books in the shelf
= 7/18
P(B) = Number of books in GK shelf / Total number of books in the shelf
= 5/18
Using the formula for finding the probability of intersection of two events, we can find the probability of A' ∩ B' as:
P(A' ∩ B') = 1 - P(A ∪ B)
where P(A ∪ B) represents the probability of the book picked up being either from Banking awareness or from GK or both.
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
where P(A ∩ B) represents the probability of the book picked up being both from Banking awareness and from GK.
We can find P(A ∩ B) as:
P(A ∩ B) = Number of books that are both in Banking awareness and GK shelf / Total number of books in the shelf
= 0 (since there are no books that are both in Banking awareness and GK shelf)
Substituting the values, we get:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
= 7/18 + 5/18 - 0
= 12/18
= 2/3
Therefore, P(A' ∩ B') = 1 - P(A ∪ B)
= 1 - 2/3
= 1/3
Hence, the probability that the book picked up is neither in Banking awareness nor in GK is 1/3.
Therefore, the correct answer is option C) 1/3.
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