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The overall percentage of failure in a certain examination is 0.30. What is the probability that out of a group of 6 candidates at least 4 passed the examination?
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The overall percentage of failure in a certain examination is 0.30. Wh...
Solution:
Given,
Overall percentage of failure in a certain examination is 0.30.
Hence, the probability of failure in an examination is 0.30.
To find:
The probability that out of a group of 6 candidates at least 4 passed the examination.
Approach:
We will use the binomial distribution formula to solve this problem.
Binomial Distribution Formula:
P(X = x) = nCx * p^x * q^(n-x)
Where,
n = number of trials
x = number of successes
p = probability of success
q = probability of failure
nCx = n! / (x! * (n-x)!)
Let's solve this problem step by step.
Step 1:
Let's find the probability of passing an examination.
p = 1 - 0.30 (as the probability of failure is given)
p = 0.70
Step 2:
Let's find the probability of at least 4 candidates passing the examination.
P(X ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6)
Where,
X = number of candidates passing the examination
P(X = x) = nCx * p^x * q^(n-x)
For x = 4,
P(X = 4) = 6C4 * 0.70^4 * 0.30^2
P(X = 4) = 0.324135
For x = 5,
P(X = 5) = 6C5 * 0.70^5 * 0.30^1
P(X = 5) = 0.302526
For x = 6,
P(X = 6) = 6C6 * 0.70^6 * 0.30^0
P(X = 6) = 0.117649
P(X ≥ 4) = 0.324135 + 0.302526 + 0.117649
P(X ≥ 4) = 0.744310
Hence, the probability that out of a group of 6 candidates at least 4 passed the examination is 0.744310 or 74.43%.
Given,
Overall percentage of failure in a certain examination is 0.30.
Hence, the probability of failure in an examination is 0.30.
To find:
The probability that out of a group of 6 candidates at least 4 passed the examination.
Approach:
We will use the binomial distribution formula to solve this problem.
Binomial Distribution Formula:
P(X = x) = nCx * p^x * q^(n-x)
Where,
n = number of trials
x = number of successes
p = probability of success
q = probability of failure
nCx = n! / (x! * (n-x)!)
Let's solve this problem step by step.
Step 1:
Let's find the probability of passing an examination.
p = 1 - 0.30 (as the probability of failure is given)
p = 0.70
Step 2:
Let's find the probability of at least 4 candidates passing the examination.
P(X ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6)
Where,
X = number of candidates passing the examination
P(X = x) = nCx * p^x * q^(n-x)
For x = 4,
P(X = 4) = 6C4 * 0.70^4 * 0.30^2
P(X = 4) = 0.324135
For x = 5,
P(X = 5) = 6C5 * 0.70^5 * 0.30^1
P(X = 5) = 0.302526
For x = 6,
P(X = 6) = 6C6 * 0.70^6 * 0.30^0
P(X = 6) = 0.117649
P(X ≥ 4) = 0.324135 + 0.302526 + 0.117649
P(X ≥ 4) = 0.744310
Hence, the probability that out of a group of 6 candidates at least 4 passed the examination is 0.744310 or 74.43%.
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The overall percentage of failure in a certain examination is 0.30. What is the probability that out of a group of 6 candidates at least 4 passed the examination?
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The overall percentage of failure in a certain examination is 0.30. What is the probability that out of a group of 6 candidates at least 4 passed the examination? 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 The overall percentage of failure in a certain examination is 0.30. What is the probability that out of a group of 6 candidates at least 4 passed the examination? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The overall percentage of failure in a certain examination is 0.30. What is the probability that out of a group of 6 candidates at least 4 passed the examination?.
The overall percentage of failure in a certain examination is 0.30. What is the probability that out of a group of 6 candidates at least 4 passed the examination? 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 The overall percentage of failure in a certain examination is 0.30. What is the probability that out of a group of 6 candidates at least 4 passed the examination? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The overall percentage of failure in a certain examination is 0.30. What is the probability that out of a group of 6 candidates at least 4 passed the examination?.
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