By rewriting the formula for the multiplication rule, you can write a formula for finding conditional probabilities. The conditional probability of event B occurring, given that event A has occurred, is P(B| A)=- the probability that a flight departed on time given that it arrives on time. P(A and B) P(A) The probability that an airplane flight departs on time is 0.91. The probability that a flight arrives on time is 0.88. The probability that a flight departs and arrives on time is 0.82. The probability that a flight departed on time given that it arrives on time is. (Round to the nearest thousandth as needed.) Use the information below to find
By rewriting the formula for the multiplication rule, you can write a formula for finding conditional probabilities. The conditional probability of event B occurring, given that event A has occurred, is P(B| A)=- the probability that a flight departed on time given that it arrives on time. P(A and B) P(A) The probability that an airplane flight departs on time is 0.91. The probability that a flight arrives on time is 0.88. The probability that a flight departs and arrives on time is 0.82. The probability that a flight departed on time given that it arrives on time is. (Round to the nearest thousandth as needed.) Use the information below to find
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Conditional Probability and Flight Arrivals
When studying probabilities, it's essential to understand how to calculate conditional probabilities. A conditional probability is the likelihood of an event occurring given that another related event has already occurred. This can be denoted and calculated using the formula:
\[ P(B \mid A) = \frac{P(A \text{ and } B)}{P(A)} \]
where \( P(B \mid A) \) is the probability of event B occurring given that event A has already happened.
#### Example Problem
Consider the scenario of calculating the probability that a flight departed on time given that it arrives on time. We are provided with the following probabilities:
- \( P(\text{Flight departs on time}) = 0.91 \)
- \( P(\text{Flight arrives on time}) = 0.88 \)
- \( P(\text{Flight departs and arrives on time}) = 0.82 \)
Using the formula for conditional probability, we need to find the probability that a flight departed on time given that it arrives on time.
#### Calculation
Plugging in the values given:
\[ P(\text{Depart on time} \mid \text{Arrive on time}) = \frac{P(\text{Depart and Arrive on time})}{P(\text{Arrive on time})} \]
\[ P(\text{Depart on time} \mid \text{Arrive on time}) = \frac{0.82}{0.88} \]
This calculation yields:
\[ P(\text{Depart on time} \mid \text{Arrive on time}) \approx 0.932 \]
So, the probability that a flight departed on time given that it arrives on time is approximately \( 0.932 \). (Round this value to the nearest thousandth as needed.)
This example helps illustrate the application of conditional probabilities in real-world scenarios, such as assessing flight performance metrics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faac5394c-8668-402c-9675-97ec190199e7%2F2cc38aa8-26fc-4ac2-bd18-ec316aa4b50b%2Fd5oxu0m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Conditional Probability and Flight Arrivals
When studying probabilities, it's essential to understand how to calculate conditional probabilities. A conditional probability is the likelihood of an event occurring given that another related event has already occurred. This can be denoted and calculated using the formula:
\[ P(B \mid A) = \frac{P(A \text{ and } B)}{P(A)} \]
where \( P(B \mid A) \) is the probability of event B occurring given that event A has already happened.
#### Example Problem
Consider the scenario of calculating the probability that a flight departed on time given that it arrives on time. We are provided with the following probabilities:
- \( P(\text{Flight departs on time}) = 0.91 \)
- \( P(\text{Flight arrives on time}) = 0.88 \)
- \( P(\text{Flight departs and arrives on time}) = 0.82 \)
Using the formula for conditional probability, we need to find the probability that a flight departed on time given that it arrives on time.
#### Calculation
Plugging in the values given:
\[ P(\text{Depart on time} \mid \text{Arrive on time}) = \frac{P(\text{Depart and Arrive on time})}{P(\text{Arrive on time})} \]
\[ P(\text{Depart on time} \mid \text{Arrive on time}) = \frac{0.82}{0.88} \]
This calculation yields:
\[ P(\text{Depart on time} \mid \text{Arrive on time}) \approx 0.932 \]
So, the probability that a flight departed on time given that it arrives on time is approximately \( 0.932 \). (Round this value to the nearest thousandth as needed.)
This example helps illustrate the application of conditional probabilities in real-world scenarios, such as assessing flight performance metrics.
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