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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?
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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.
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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?
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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?.
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