12. Suppose that P(E)=0.82, P(F)=0.63, and P(EF) = 0.12. Find the following:
A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Question
A) 0.800
B) 0.940
C) 0.794
D) 0.410
E) 0.060
![**Problem 12:**
Suppose that \( P(E) = 0.82 \), \( P(F) = 0.63 \), and \( P(E^c \cap F) = 0.12 \). Find the following:
(No graphs or diagrams are present in this image. It's a simple mathematical problem related to probability involving events \( E \) and \( F \).)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F92c2922e-f052-407b-a27f-aa2447c0b3a1%2Fc70abeda-6f24-4b6e-998c-6ef8572d8c31%2F91vgbj_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 12:**
Suppose that \( P(E) = 0.82 \), \( P(F) = 0.63 \), and \( P(E^c \cap F) = 0.12 \). Find the following:
(No graphs or diagrams are present in this image. It's a simple mathematical problem related to probability involving events \( E \) and \( F \).)
![F. \( P(E^c \cap F^c) \)
This expression represents the probability of the intersection of the complements of events E and F. In probability, the complement of an event E (denoted as \( E^c \)) includes all outcomes in the sample space that are not in E. Similarly, \( F^c \) is the complement of event F.
The intersection of \( E^c \) and \( F^c \) (denoted as \( E^c \cap F^c \)) includes all outcomes that are neither in event E nor in event F. The probability, \( P(E^c \cap F^c) \), is thus the likelihood that neither event E nor event F occurs.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F92c2922e-f052-407b-a27f-aa2447c0b3a1%2Fc70abeda-6f24-4b6e-998c-6ef8572d8c31%2F2zr0wug_processed.png&w=3840&q=75)
Transcribed Image Text:F. \( P(E^c \cap F^c) \)
This expression represents the probability of the intersection of the complements of events E and F. In probability, the complement of an event E (denoted as \( E^c \)) includes all outcomes in the sample space that are not in E. Similarly, \( F^c \) is the complement of event F.
The intersection of \( E^c \) and \( F^c \) (denoted as \( E^c \cap F^c \)) includes all outcomes that are neither in event E nor in event F. The probability, \( P(E^c \cap F^c) \), is thus the likelihood that neither event E nor event F occurs.
Expert Solution
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Step 1: Given that
P(E)=0.82 ,P(F)=0.63
and P(Ec ∩ F)=0.12
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Solved in 3 steps with 1 images
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