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An animal shelter has kittens and adult cats available for adoption. Suppose that 30% of all cats are kittens. Probability of adoption for a kitten is 0.8, whereas the probability of adoption for an adult cat is only 0.6. On the other hand, 20% of all cats are black and the probability of adoption for a black cat is 0.1. (a) What is the probability of adoption for a randomly chosen cat? (b) If a cat is adopted, what is the probability that it is a kitten? (c) What is the probability of adoption for a non-black cat? (d) Is the adoption chances of a cat is dependent on its coloring? Justify your answer mathematically.

An animal shelter has kittens and adult cats available for adoption. Suppose that 30% of all cats are kittens. Probability of adoption for a kitten is 0.8, whereas the probability of adoption for an adult cat is only 0.6. On the other hand, 20% of all cats are black and the probability of adoption for a black cat is 0.1. (a) What is the probability of adoption for a randomly chosen cat? (b) If a cat is adopted, what is the probability that it is a kitten? (c) What is the probability of adoption for a non-black cat? (d) Is the adoption chances of a cat is dependent on its coloring? Justify your answer mathematically.

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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An animal shelter has kittens and adult cats available for adoption. Suppose that 30% of all cats are kittens. Probability of adoption for a kitten is 0.8, whereas the probability of adoption for an adult cat is only 0.6. On the other hand, 20% of all cats are black and the probability of adoption for a black cat is 0.1. (a) What is the probability of adoption for a randomly chose cat? (b) If a cat is adopted, what is the probability that it is a kitten? (c) What is the probability of adoption for a non-black cat? (d) Is the adoption chances of a cat is dependent on its coloring? Justify your answer mathematically.
Transcribed Image Text:An animal shelter has kittens and adult cats available for adoption. Suppose that 30% of all cats are kittens. Probability of adoption for a kitten is 0.8, whereas the probability of adoption for an adult cat is only 0.6. On the other hand, 20% of all cats are black and the probability of adoption for a black cat is 0.1. (a) What is the probability of adoption for a randomly chose cat? (b) If a cat is adopted, what is the probability that it is a kitten? (c) What is the probability of adoption for a non-black cat? (d) Is the adoption chances of a cat is dependent on its coloring? Justify your answer mathematically.
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)
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