Question

6. A group of dogs consists of four brown males, two brown females, six white males, four white females, five black males, and four black females.   

(a) What is the probability of selecting at random a brown female dog?

(b) What is the conditional probability of selecting at random a female dog, if the dog is brown?

(c) What is the conditional probability of selecting at random a brown dog, if the dog is a female?

PLEASE SHOW STEPS AND EXPLAIN

Answer 1

Total dogs = 4 + 2 + 6 + 4 + 5 + 4 = 25

a) Probability of selecting at random a brown female dog is computed here as:

= Number of ways to select a brown female dog / Total dogs

= 2/25

= 0.08

Therefore 0.08 is the required probability here.

b) Given that the dog is brown, the probability of selecting at random a female dog is computed using Bayes theorem here as:

= Number of female brown dog / Total number of brown dogs

= 2/6

= 1/3

Therefore 0.3333 is the required probability here.

c) Given that the dog is female, the probability of selecting a random brown dog is computed here as:

= Number of female brown dogs / Total number of female dogs

= 2/10

= 0.2

Therefore 0.2 is the required probability here.