CA Foundation Exam > CA Foundation Questions > A renowned hospital usually admits 200 patien...
Start Learning for Free
A renowned hospital usually admits 200 patients every day. One per cent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities?a)0.1428b)0.1732c)0.2235d)0.3450?
Most Upvoted Answer
A renowned hospital usually admits 200 patients every day. One per cen...
Given:
- The hospital usually admits 200 patients every day.
- 1% of the patients, on average, require special room facilities.
- Only one special room is available on a particular morning.
To find the probability that more than 3 patients would require special room facilities, we can use the binomial distribution.
Binomial Distribution:
The binomial distribution is used to calculate the probability of a certain number of successes in a fixed number of independent Bernoulli trials, where each trial has the same probability of success.
The probability mass function for the binomial distribution is given by:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
- P(X = k) is the probability of getting exactly k successes.
- C(n, k) is the number of combinations of n items taken k at a time (n choose k).
- p is the probability of success on each trial.
- n is the number of trials.
In this case:
- n = 200 (number of patients admitted every day)
- p = 0.01 (probability of a patient requiring special room facilities)
- k > 3 (more than 3 patients requiring special room facilities)
Calculating the Probability:
To find the probability that more than 3 patients would require special room facilities, we need to calculate the sum of probabilities for k = 4, 5, 6, ..., 200.
P(X > 3) = 1 - P(X ≤ 3)
P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
Calculating P(X = 0):
P(X = 0) = C(200, 0) * (0.01)^0 * (1-0.01)^(200-0)
Calculating P(X = 1), P(X = 2), and P(X = 3) using the same formula.
Finally, calculating P(X > 3) using the formula P(X > 3) = 1 - P(X ≤ 3).
Final Answer:
The calculated probability of more than 3 patients requiring special room facilities is the answer to the question.
Therefore, the correct answer is option (c) 0.2235.
- The hospital usually admits 200 patients every day.
- 1% of the patients, on average, require special room facilities.
- Only one special room is available on a particular morning.
To find the probability that more than 3 patients would require special room facilities, we can use the binomial distribution.
Binomial Distribution:
The binomial distribution is used to calculate the probability of a certain number of successes in a fixed number of independent Bernoulli trials, where each trial has the same probability of success.
The probability mass function for the binomial distribution is given by:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
- P(X = k) is the probability of getting exactly k successes.
- C(n, k) is the number of combinations of n items taken k at a time (n choose k).
- p is the probability of success on each trial.
- n is the number of trials.
In this case:
- n = 200 (number of patients admitted every day)
- p = 0.01 (probability of a patient requiring special room facilities)
- k > 3 (more than 3 patients requiring special room facilities)
Calculating the Probability:
To find the probability that more than 3 patients would require special room facilities, we need to calculate the sum of probabilities for k = 4, 5, 6, ..., 200.
P(X > 3) = 1 - P(X ≤ 3)
P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
Calculating P(X = 0):
P(X = 0) = C(200, 0) * (0.01)^0 * (1-0.01)^(200-0)
Calculating P(X = 1), P(X = 2), and P(X = 3) using the same formula.
Finally, calculating P(X > 3) using the formula P(X > 3) = 1 - P(X ≤ 3).
Final Answer:
The calculated probability of more than 3 patients requiring special room facilities is the answer to the question.
Therefore, the correct answer is option (c) 0.2235.
Attention CA Foundation Students!
To make sure you are not studying endlessly, EduRev has designed CA Foundation study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CA Foundation.
|
Explore Courses for CA Foundation exam
|
|
Similar CA Foundation Doubts
Top Courses for CA FoundationView all
A renowned hospital usually admits 200 patients every day. One per cent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities?a)0.1428b)0.1732c)0.2235d)0.3450?
Question Description
A renowned hospital usually admits 200 patients every day. One per cent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities?a)0.1428b)0.1732c)0.2235d)0.3450? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A renowned hospital usually admits 200 patients every day. One per cent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities?a)0.1428b)0.1732c)0.2235d)0.3450? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A renowned hospital usually admits 200 patients every day. One per cent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities?a)0.1428b)0.1732c)0.2235d)0.3450?.
A renowned hospital usually admits 200 patients every day. One per cent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities?a)0.1428b)0.1732c)0.2235d)0.3450? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A renowned hospital usually admits 200 patients every day. One per cent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities?a)0.1428b)0.1732c)0.2235d)0.3450? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A renowned hospital usually admits 200 patients every day. One per cent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities?a)0.1428b)0.1732c)0.2235d)0.3450?.
Solutions for A renowned hospital usually admits 200 patients every day. One per cent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities?a)0.1428b)0.1732c)0.2235d)0.3450? in English & in Hindi are available as part of our courses for CA Foundation.
Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of A renowned hospital usually admits 200 patients every day. One per cent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities?a)0.1428b)0.1732c)0.2235d)0.3450? defined & explained in the simplest way possible. Besides giving the explanation of
A renowned hospital usually admits 200 patients every day. One per cent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities?a)0.1428b)0.1732c)0.2235d)0.3450?, a detailed solution for A renowned hospital usually admits 200 patients every day. One per cent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities?a)0.1428b)0.1732c)0.2235d)0.3450? has been provided alongside types of A renowned hospital usually admits 200 patients every day. One per cent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities?a)0.1428b)0.1732c)0.2235d)0.3450? theory, EduRev gives you an
ample number of questions to practice A renowned hospital usually admits 200 patients every day. One per cent patients, on an average, require special room facilities. On one particular morning, it was found that only one special room is available. What is the probability that more than 3 patients would require special room facilities?a)0.1428b)0.1732c)0.2235d)0.3450? tests, examples and also practice CA Foundation tests.
|
|
Explore Courses for CA Foundation exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup