In guinea pig, short hair (L) is dominant to long hair (l) and the heterozygous condition for yellow coat (Y) and white coat (y) gives cream coat. A short haired guinea pig is bred to long haired white guinea pig and one of the offspring is a long haired baby guinea pig.

a. What is the probability that an offspring will be recessive for both gene pairs?
b. What is the probability that a short haired white guinea pig will be produced?
(Show solutions)

To solve these questions, we can use Punnett squares to determine the possible genotypes and phenotypes of the offspring.

First, let's list the given genes and their possible alleles:

- Hair Length: Short hair (L) is dominant over long hair (l).
- Coat Color: Yellow coat (Y) is dominant over white coat (y), and the heterozygous condition (Yy) results in a cream coat.

Now let's answer each question:

a. What is the probability that an offspring will be recessive for both gene pairs?

To determine the probability of an offspring being recessive for both gene pairs, we need to consider the genotype of the parents.

The short-haired guinea pig can have two possible genotypes: heterozygous (Ll) or homozygous dominant (LL). Since we don't have this information, we'll consider both possibilities separately.

For the long-haired white guinea pig, we know its genotype is homozygous recessive for hair length (ll) and homozygous recessive for coat color (yy).

Let's start with the first possibility:
Parent 1: Short-haired guinea pig with genotype L_
Parent 2: Long-haired white guinea pig with genotype ll, yy

Using a Punnett square, we can determine the possible genotypes and phenotypes of their offspring:

L l
----------------
l | Ll | ll |
----------------
y | Ly | ly |
----------------

From the Punnett square above, we can see that there are only 2 possible combinations (Ly and ly) that would result in recessive genotypes for both gene pairs (ll, ly).

Therefore, the probability of an offspring being recessive for both gene pairs is 2 out of 4, or 1/2 (50%).

b. What is the probability that a short-haired white guinea pig will be produced?

To determine the probability of a short-haired white guinea pig, we need to consider the genotype of the parents again.

Using the same Punnett square from the previous question, we can see that there is only 1 possible combination (Ly) that would result in a short-haired white guinea pig (Ly).

Therefore, the probability of a short-haired white guinea pig being produced is 1 out of 4, or 1/4 (25%).