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A concession stand at a movie theater offers soda and popcorn for sale. A survey shows tha 50% of moviegoers purchase a soda, 45% of moviegoers purchase popcorn, and 25% of the mov purchase both soda and popcorn. We define the following events for a randomly chosen moviegoer: A:purchases a soda B: purchases popcorn

A concession stand at a movie theater offers soda and popcorn for sale. A survey shows tha 50% of moviegoers purchase a soda, 45% of moviegoers purchase popcorn, and 25% of the mov purchase both soda and popcorn. We define the following events for a randomly chosen moviegoer: A:purchases a soda B: purchases popcorn

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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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Please answer correctly and show all your work. Attached is the formula sheet you can use.
Axioms of Probability Also Note: 1. P(S)=1 For any two events A and B, 2. For any event E, 0< P(E) < 1 P(A) = P(AN B) + P(AN B') 3. For any two mutually exclusive events, and P(EUF) = P(E)+ P(F) P(AN B) P(A|B)P(B). Events A and B are independent if: Addition Rule P(EUF) = P(E)+ P(F) – P(EnF) P(A|B) = P(A) or Conditional Probability P(AN B) = P(A)P(B). Р(BJA) — P(ANB) P(A) Bayes' Theorem: Total Probability Rule Р(A В)P(В) Р(А|B)Р(В) + Р(A|B')P(В') P(A) = P(A|B)P(B)+P(A|B')P(B') P(B|A) Similarly, Similarly, P(A) =P(A|E1)P(E1) + P(A|E2)P(E2)+ ...+ P(A|Ek)P(Ek) P(B|E1)P(E1) P(B|E1)P(E1) + P(B|E2)P(E2) + · .+ P(B|ER)P(Ex) P(E1|B)
Transcribed Image Text:Axioms of Probability Also Note: 1. P(S)=1 For any two events A and B, 2. For any event E, 0< P(E) < 1 P(A) = P(AN B) + P(AN B') 3. For any two mutually exclusive events, and P(EUF) = P(E)+ P(F) P(AN B) P(A|B)P(B). Events A and B are independent if: Addition Rule P(EUF) = P(E)+ P(F) – P(EnF) P(A|B) = P(A) or Conditional Probability P(AN B) = P(A)P(B). Р(BJA) — P(ANB) P(A) Bayes' Theorem: Total Probability Rule Р(A В)P(В) Р(А|B)Р(В) + Р(A|B')P(В') P(A) = P(A|B)P(B)+P(A|B')P(B') P(B|A) Similarly, Similarly, P(A) =P(A|E1)P(E1) + P(A|E2)P(E2)+ ...+ P(A|Ek)P(Ek) P(B|E1)P(E1) P(B|E1)P(E1) + P(B|E2)P(E2) + · .+ P(B|ER)P(Ex) P(E1|B)
.A concession stand at a movie theater offers soda and popcorn for sale. A survey shows that that 50% of moviegoers purchase a soda, 45% of moviegoers purchase popcorn, and 25% of the moviegoers purchase both soda and popcorn. We define the following events for a randomly chosen moviegoer: A:purchases a soda B: purchases popcorn
Transcribed Image Text:.A concession stand at a movie theater offers soda and popcorn for sale. A survey shows that that 50% of moviegoers purchase a soda, 45% of moviegoers purchase popcorn, and 25% of the moviegoers purchase both soda and popcorn. We define the following events for a randomly chosen moviegoer: A:purchases a soda B: purchases popcorn
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