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?

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)

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

Hence, the required probability is 0.1923.

its 50 miles away from the starting point

noncoplanar points are points that do not lie on the same line.