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A graduating student keeps applying for jobs until she has 3 offers. The probability of getting an offer at any trial is 0.48. What is the probability that: 4) She gets 3 offers out of six applications, b) She gets at least one offer in response to 3 applications. The manber of rescue calls received by a rescue squad in a city follows a Poisson distribution?
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A graduating student keeps applying for jobs until she has 3 offers. T...
Probability of Getting 3 Offers:
- The probability of getting an offer at any trial is 0.48.
- This means the probability of not getting an offer is 1 - 0.48 = 0.52.
- To find the probability of getting 3 offers out of 6 applications, we use the binomial probability formula:
P(X = k) = (n choose k) * p^k * (1 - p)^(n-k), where n is the number of trials, k is the number of successful trials, and p is the probability of success.
- In this case, n = 6, k = 3, p = 0.48.
- Calculating the probability: P(X = 3) = (6 choose 3) * 0.48^3 * 0.52^3 = 0.3121 or 31.21%.
Probability of Getting At Least One Offer:
- To find the probability of getting at least one offer in response to 3 applications, we can find the complement of the probability of getting no offers.
- The probability of getting no offer in one trial is 1 - 0.48 = 0.52.
- So, the probability of getting no offers in 3 trials is 0.52^3 = 0.1406.
- Therefore, the probability of getting at least one offer is 1 - 0.1406 = 0.8594 or 85.94%.
Poisson Distribution Explanation:
- The number of rescue calls received by a rescue squad in a city follows a Poisson distribution if the following conditions are met:
- The number of calls received in disjoint time intervals are independent of each other.
- The average rate of calls remains constant over time.
- The probability of more than one call in a very small time interval is negligible.
- The Poisson distribution is characterized by one parameter, λ (lambda), which represents the average rate of occurrence.
- The probability of observing k events in a fixed interval of time or space is given by the Poisson probability mass function:
P(X = k) = (e^(-λ) * λ^k) / k!, where k is the number of events, e is the base of the natural logarithm, and k! is the factorial of k.
- The Poisson distribution is commonly used in scenarios where events occur at a constant average rate, such as the number of calls received by a rescue squad in a city.
- The probability of getting an offer at any trial is 0.48.
- This means the probability of not getting an offer is 1 - 0.48 = 0.52.
- To find the probability of getting 3 offers out of 6 applications, we use the binomial probability formula:
P(X = k) = (n choose k) * p^k * (1 - p)^(n-k), where n is the number of trials, k is the number of successful trials, and p is the probability of success.
- In this case, n = 6, k = 3, p = 0.48.
- Calculating the probability: P(X = 3) = (6 choose 3) * 0.48^3 * 0.52^3 = 0.3121 or 31.21%.
Probability of Getting At Least One Offer:
- To find the probability of getting at least one offer in response to 3 applications, we can find the complement of the probability of getting no offers.
- The probability of getting no offer in one trial is 1 - 0.48 = 0.52.
- So, the probability of getting no offers in 3 trials is 0.52^3 = 0.1406.
- Therefore, the probability of getting at least one offer is 1 - 0.1406 = 0.8594 or 85.94%.
Poisson Distribution Explanation:
- The number of rescue calls received by a rescue squad in a city follows a Poisson distribution if the following conditions are met:
- The number of calls received in disjoint time intervals are independent of each other.
- The average rate of calls remains constant over time.
- The probability of more than one call in a very small time interval is negligible.
- The Poisson distribution is characterized by one parameter, λ (lambda), which represents the average rate of occurrence.
- The probability of observing k events in a fixed interval of time or space is given by the Poisson probability mass function:
P(X = k) = (e^(-λ) * λ^k) / k!, where k is the number of events, e is the base of the natural logarithm, and k! is the factorial of k.
- The Poisson distribution is commonly used in scenarios where events occur at a constant average rate, such as the number of calls received by a rescue squad in a city.
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A graduating student keeps applying for jobs until she has 3 offers. The probability of getting an offer at any trial is 0.48. What is the probability that: 4) She gets 3 offers out of six applications, b) She gets at least one offer in response to 3 applications. The manber of rescue calls received by a rescue squad in a city follows a Poisson distribution?
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A graduating student keeps applying for jobs until she has 3 offers. The probability of getting an offer at any trial is 0.48. What is the probability that: 4) She gets 3 offers out of six applications, b) She gets at least one offer in response to 3 applications. The manber of rescue calls received by a rescue squad in a city follows a Poisson distribution? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A graduating student keeps applying for jobs until she has 3 offers. The probability of getting an offer at any trial is 0.48. What is the probability that: 4) She gets 3 offers out of six applications, b) She gets at least one offer in response to 3 applications. The manber of rescue calls received by a rescue squad in a city follows a Poisson distribution? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A graduating student keeps applying for jobs until she has 3 offers. The probability of getting an offer at any trial is 0.48. What is the probability that: 4) She gets 3 offers out of six applications, b) She gets at least one offer in response to 3 applications. The manber of rescue calls received by a rescue squad in a city follows a Poisson distribution?.
A graduating student keeps applying for jobs until she has 3 offers. The probability of getting an offer at any trial is 0.48. What is the probability that: 4) She gets 3 offers out of six applications, b) She gets at least one offer in response to 3 applications. The manber of rescue calls received by a rescue squad in a city follows a Poisson distribution? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A graduating student keeps applying for jobs until she has 3 offers. The probability of getting an offer at any trial is 0.48. What is the probability that: 4) She gets 3 offers out of six applications, b) She gets at least one offer in response to 3 applications. The manber of rescue calls received by a rescue squad in a city follows a Poisson distribution? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A graduating student keeps applying for jobs until she has 3 offers. The probability of getting an offer at any trial is 0.48. What is the probability that: 4) She gets 3 offers out of six applications, b) She gets at least one offer in response to 3 applications. The manber of rescue calls received by a rescue squad in a city follows a Poisson distribution?.
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