A breeder has 18 puppies for sale of which 8 are yellow labrador retrievers. if 4 puppies are selected at random, determine the probability that they are all yellow labrador retrievers. assume that selection is to be done without replacement.

The correct answer is that the probability of selecting randomly 4 yellow Labrador retriever puppies is 7/306 or 2.29% (Rounding to two decimals)

Step-by-step explanation:

1. First selection:

Probability of selecting a yellow puppy = Number of yellow Labrador retrievers / Total of puppies

Probability of selecting a 1st yellow puppy = 8 / 18

Probability of selecting a 1st yellow Labrador retriever puppy = 4 / 9

2. Second selection:

Probability of selecting a 2nd yellow puppy = Number of yellow Labrador retrievers / Total of puppies * Probability of selecting a 1st yellow puppy

Probability of selecting a 2nd yellow puppy = 7 / 17 (No replacement and now we just have 17 puppies and 7 yellow puppies) * 4/9

Probability of selecting a 2nd yellow Labrador retriever puppy without replacement = 28/153

3. Third selection:

Probability of selecting a 3rd yellow puppy = Number of yellow Labrador retrievers / Total of puppies * Probability of selecting a 1st yellow puppy * Probability of selecting a 2nd yellow puppy

Probability of selecting a 3rd yellow puppy = 6 / 16 (No replacement and now we just have 16 puppies and 6 yellow puppies) * 4/9 * 7/17

6/16 * 4/9 * 7/17 = 3/8 * 4/9 * 7/17 = (1 * 1 * 7) / (2 * 3 * 17) = 7/102 (Simplifying)

Probability of selecting a 3rd yellow Labrador retriever puppy without replacement = 7/102

4. Fourth and final selection:

Probability of selecting a 4th yellow puppy = Number of yellow Labrador retrievers / Total of puppies * Probability of selecting a 1st yellow puppy * Probability of selecting a 2nd yellow puppy * Probability of selecting a 3rd yellow puppy

Probability of selecting a 4th yellow puppy = 5 / 15 (No replacement and now we just have 15 puppies and 5 yellow puppies) * 4/9 * 7/17 * 3/8

5/15 * 3/8 * 4/9 * 7/17 = 1/3 * 3/8 * 4/9 * 7/17 = (1 * 1 * 1 * 7) / (3 * 2 * 3 * 17) = 7/306 (Simplifying)

Probability of selecting a 4th yellow Labrador retriever puppy without replacement = 7/306