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.

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Mathematics

31 August, 08:03

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.

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Alf · Answer 1

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