Question

A certain unsavory bar for poker-playing dogs is attended by only two types of dogs: "good dogs" and "bad dogs." For a randomly selected dog in the bar, the probability it’s a good dog is 40%. The probability the dog smokes, given that it’s a bad dog is 70%; the probability it smokes given that it’s a good dog is 25%.
You walk into the bar and observe a dog smoking a pipe. What the probability it is actually a good dog?

Answer 1

Answer:

its is a good dog

Step-by-step explanation:

Answer 2

Answer: The required probability is 0.1923.

Step-by-step explanation:

Since we have given that

Probability that it's a good dog = 0.4

Probability that it's a bad dog = 1-0.4 = 0.6

Probability that the dog smokes given that its a bad dog = 0.7

Probability that it smokes given that its a good dog = 0.25

According to question, probability of smoking pipe would be

P(good).P(Smoking pipe|good)+P(bad).P(smoking pipe|bad)

$0.4\times 0.25+0.6\times 0.7\\\\=0.1+0.42\\\\=0.52$

So, Probability of getting a good dog given that it is smoking pipe is given by

$\dfrac{P(good).P(smoking\ pipe|good)}{P(smoking\ pipe)}\\\\=\dfrac{0.4\times 0.25}{0.52}\\\\=\dfrac{0.1}{0.52}\\\\=0.1923$

Hence, the required probability is 0.1923.