Homework Help is Here – Start Your Trial Now!
Math
Probability
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.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
See similar textbooks
icon
Related questions
Question
Please answer correctly and show all your work. Attached is the formula sheet you can use.
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)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer