Below is a transcription of the provided image, designed for educational purposes. The content includes probabilities and requires the application of conditional probability formulas.---**Probability Problem**Given:- \( P(E) = 0.85 \)- \( P(F) = 0.23 \)- \( P(E \cup F) = 0.94 \)Find:- (a) \( P(E | F) \)- (b) \( P(F | E) \)---(a) \( P(E | F) = \) [ ](Type an integer or decimal rounded to two decimal places as needed.)---(b) \( P(F | E) = \) [ ](Type an integer or decimal rounded to two decimal places as needed.)---**Explanation:**- \( P(E | F) \) represents the probability of event E occurring given that event F has occurred.- \( P(F | E) \) represents the probability of event F occurring given that event E has occurred.To solve these problems, you will need to apply the definitions of conditional probability:\[ P(E | F) = \frac{P(E \cap F)}{P(F)} \]\[ P(F | E) = \frac{P(F \cap E)}{P(E)} \]Since the union of E and F is provided, you may need to calculate the intersection \( P(E \cap F) \):\[ P(E \cap F) = P(E) + P(F) - P(E \cup F) \]---There are no graphs or diagrams to explain in this image.

Answered: Image /qna-images/answer/5cfa61f1-a168-4df8-8ac9-2ced7f80c83e.jpg

Answered: Let P(E)=0.85, P(F) = 0.23, and P(EUF)…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let P(E)=0.85, P(F) = 0.23, and P(EUF) = 0.94. Find (a) P(EIF) and (b) P(FIE). (a) P(EIF) = (Type an integer or decimal rounded to two decimal places as needed.) (b) P(FIE) = (Type an integer or decimal rounded to two decimal places as needed.) ...