Answer:
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
