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In a certain town, the probability that it will rain in the afternoon is known to be 0.6. Moreover, meteorological data indicates that if the temperature at noon is less than or equal to 250C, the probability that it will rain in the afternoon is 0.4. The temperature at noon is equally likely to be above 250C, or at/below 250C.
What is the probability that it will rain in the afternoon on a day when the temperature at noon is above 250C?
What is the probability that it will rain in the afternoon on a day when the temperature at noon is above 250C?
- a)0.4
- b)0.6
- c)0.8
- d)0.9
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
In a certain town, the probability that it will rain in the afternoon ...
Let RA : Rain in the afternoon
T > 25 : Temperature more than 250C
Let the desired probability = P(RAIT ≤ 25) = x
The tree diagram forthis problem is given below:
Given P(RA) = 0.6
by rule of total probability P(RA)
⇒ x = 0.8
T > 25 : Temperature more than 250C
Let the desired probability = P(RAIT ≤ 25) = x
The tree diagram forthis problem is given below:
Given P(RA) = 0.6
by rule of total probability P(RA)
⇒ x = 0.8
Most Upvoted Answer
In a certain town, the probability that it will rain in the afternoon ...
Given Information:
- Probability of rain in the afternoon = 0.6
- Probability of rain in the afternoon if temperature at noon is <= 25°c="">
- Temperature at noon is equally likely to be above 25°C or at/below 25°C
To Find:
Probability of rain in the afternoon when temperature at noon is above 25°C
Solution:
Let's denote the events as follows:
- R = Rain in the afternoon
- T = Temperature at noon is above 25°C
We are given that P(R) = 0.6 and P(R|T ≤ 25°C) = 0.4.
We need to find P(R|T > 25°C).
Using Bayes' Theorem:
P(R|T > 25°C) = (P(T > 25°C|R) * P(R)) / P(T > 25°C)
Calculating P(T > 25°C|R):
P(T > 25°C|R) represents the probability that the temperature at noon is above 25°C given that it is raining in the afternoon.
Since the temperature at noon is equally likely to be above 25°C or at/below 25°C, we can assume that P(T > 25°C|R) = 1 - P(T ≤ 25°C|R).
Therefore, P(T > 25°C|R) = 1 - 0.4 = 0.6.
Calculating P(T > 25°C):
P(T > 25°C) represents the probability that the temperature at noon is above 25°C.
Since the temperature at noon is equally likely to be above 25°C or at/below 25°C, we can assume that P(T > 25°C) = P(T ≤ 25°C).
Therefore, P(T > 25°C) = 1 - P(T ≤ 25°C).
Using Total Probability Theorem:
P(T > 25°C) = P(T > 25°C|R) * P(R) + P(T > 25°C|!R) * P(!R)
Since P(T > 25°C|!R) is not given, we need to calculate it using the given information.
P(T > 25°C|!R) = 1 - P(T ≤ 25°C|!R)
We are given that the probability of rain in the afternoon if the temperature at noon is ≤ 25°C is 0.4.
Therefore, P(T ≤ 25°C|!R) = 0.4.
P(T > 25°C|!R) = 1 - 0.4 = 0.6.
Calculating P(T > 25°C):
P(T > 25°C) = P(T > 25°C|R) * P(R) + P(T > 25°C|!R) * P(!R)
Since the temperature at noon is equally likely to be above 25°C or at/below 25°C, we can assume that P(!R) = 1 - P(R).
Therefore, P(T > 25°C) = P(T > 25°C|R) * P(R) + P(T > 25°C|!R) * (1
- Probability of rain in the afternoon = 0.6
- Probability of rain in the afternoon if temperature at noon is <= 25°c="">
- Temperature at noon is equally likely to be above 25°C or at/below 25°C
To Find:
Probability of rain in the afternoon when temperature at noon is above 25°C
Solution:
Let's denote the events as follows:
- R = Rain in the afternoon
- T = Temperature at noon is above 25°C
We are given that P(R) = 0.6 and P(R|T ≤ 25°C) = 0.4.
We need to find P(R|T > 25°C).
Using Bayes' Theorem:
P(R|T > 25°C) = (P(T > 25°C|R) * P(R)) / P(T > 25°C)
Calculating P(T > 25°C|R):
P(T > 25°C|R) represents the probability that the temperature at noon is above 25°C given that it is raining in the afternoon.
Since the temperature at noon is equally likely to be above 25°C or at/below 25°C, we can assume that P(T > 25°C|R) = 1 - P(T ≤ 25°C|R).
Therefore, P(T > 25°C|R) = 1 - 0.4 = 0.6.
Calculating P(T > 25°C):
P(T > 25°C) represents the probability that the temperature at noon is above 25°C.
Since the temperature at noon is equally likely to be above 25°C or at/below 25°C, we can assume that P(T > 25°C) = P(T ≤ 25°C).
Therefore, P(T > 25°C) = 1 - P(T ≤ 25°C).
Using Total Probability Theorem:
P(T > 25°C) = P(T > 25°C|R) * P(R) + P(T > 25°C|!R) * P(!R)
Since P(T > 25°C|!R) is not given, we need to calculate it using the given information.
P(T > 25°C|!R) = 1 - P(T ≤ 25°C|!R)
We are given that the probability of rain in the afternoon if the temperature at noon is ≤ 25°C is 0.4.
Therefore, P(T ≤ 25°C|!R) = 0.4.
P(T > 25°C|!R) = 1 - 0.4 = 0.6.
Calculating P(T > 25°C):
P(T > 25°C) = P(T > 25°C|R) * P(R) + P(T > 25°C|!R) * P(!R)
Since the temperature at noon is equally likely to be above 25°C or at/below 25°C, we can assume that P(!R) = 1 - P(R).
Therefore, P(T > 25°C) = P(T > 25°C|R) * P(R) + P(T > 25°C|!R) * (1
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In a certain town, the probability that it will rain in the afternoon is known to be 0.6. Moreover, meteorological data indicates that if the temperature at noon is less than or equal to 250C, the probability that it will rain in the afternoon is 0.4. The temperature at noon is equally likely to be above 250C, or at/below 250C.What is the probability that it will rain in the afternoon on a day when the temperature at noon is above 250C?a)0.4b)0.6c)0.8d)0.9Correct answer is option 'C'. Can you explain this answer?
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In a certain town, the probability that it will rain in the afternoon is known to be 0.6. Moreover, meteorological data indicates that if the temperature at noon is less than or equal to 250C, the probability that it will rain in the afternoon is 0.4. The temperature at noon is equally likely to be above 250C, or at/below 250C.What is the probability that it will rain in the afternoon on a day when the temperature at noon is above 250C?a)0.4b)0.6c)0.8d)0.9Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about In a certain town, the probability that it will rain in the afternoon is known to be 0.6. Moreover, meteorological data indicates that if the temperature at noon is less than or equal to 250C, the probability that it will rain in the afternoon is 0.4. The temperature at noon is equally likely to be above 250C, or at/below 250C.What is the probability that it will rain in the afternoon on a day when the temperature at noon is above 250C?a)0.4b)0.6c)0.8d)0.9Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a certain town, the probability that it will rain in the afternoon is known to be 0.6. Moreover, meteorological data indicates that if the temperature at noon is less than or equal to 250C, the probability that it will rain in the afternoon is 0.4. The temperature at noon is equally likely to be above 250C, or at/below 250C.What is the probability that it will rain in the afternoon on a day when the temperature at noon is above 250C?a)0.4b)0.6c)0.8d)0.9Correct answer is option 'C'. Can you explain this answer?.
In a certain town, the probability that it will rain in the afternoon is known to be 0.6. Moreover, meteorological data indicates that if the temperature at noon is less than or equal to 250C, the probability that it will rain in the afternoon is 0.4. The temperature at noon is equally likely to be above 250C, or at/below 250C.What is the probability that it will rain in the afternoon on a day when the temperature at noon is above 250C?a)0.4b)0.6c)0.8d)0.9Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about In a certain town, the probability that it will rain in the afternoon is known to be 0.6. Moreover, meteorological data indicates that if the temperature at noon is less than or equal to 250C, the probability that it will rain in the afternoon is 0.4. The temperature at noon is equally likely to be above 250C, or at/below 250C.What is the probability that it will rain in the afternoon on a day when the temperature at noon is above 250C?a)0.4b)0.6c)0.8d)0.9Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a certain town, the probability that it will rain in the afternoon is known to be 0.6. Moreover, meteorological data indicates that if the temperature at noon is less than or equal to 250C, the probability that it will rain in the afternoon is 0.4. The temperature at noon is equally likely to be above 250C, or at/below 250C.What is the probability that it will rain in the afternoon on a day when the temperature at noon is above 250C?a)0.4b)0.6c)0.8d)0.9Correct answer is option 'C'. Can you explain this answer?.
Solutions for In a certain town, the probability that it will rain in the afternoon is known to be 0.6. Moreover, meteorological data indicates that if the temperature at noon is less than or equal to 250C, the probability that it will rain in the afternoon is 0.4. The temperature at noon is equally likely to be above 250C, or at/below 250C.What is the probability that it will rain in the afternoon on a day when the temperature at noon is above 250C?a)0.4b)0.6c)0.8d)0.9Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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