Long necks in some animals are inherited as an autosomal dominant trait with 80% penetrance. Two heterozygous animals with long necks are crossed (Ll x Ll). What is the probability that their offspring will have long necks?Group of answer choices60%30%70%35%
Question
Long necks in some animals are inherited as an autosomal dominant trait with 80% penetrance. Two heterozygous animals with long necks are crossed (Ll x Ll). What is the probability that their offspring will have long necks?Group of answer choices60%30%70%35%
Solution 1
To solve this problem, we first need to understand the Punnett square for this cross.
When two heterozygous animals (Ll x Ll) are crossed, the Punnett square would look like this:
L l
L LL Ll
l Ll ll
From this, we can see that the genotypic ratio is 1 LL : 2 Ll : 1 ll.
However, we are told that the trait for long necks is an autosomal dominant trait with 80% penetrance. This means that not all animals with the dominant allele will express the trait.
So, we need to calculate the probability of the offspring having long necks, taking into account the 80% penetrance.
The probability of an offspring being LL is 1/4, and since LL will definitely have a long neck, we can say that the probability of an offspring being LL and having a long neck is 1/4.
The probability of an offspring being Ll is 2/4 or 1/2. However, since the penetrance is 80%, only 80% of these Ll offspring will have long necks. So, the probability of an offspring being Ll and having a long neck is 1/2 * 0.8 = 0.4 or 2/5.
Adding these probabilities together, the total probability of an offspring having a long neck is 1/4 (for LL) + 2/5 (for Ll) = 4/20 + 8/20 = 12/20 = 60%.
So, the probability that their offspring will have long necks is 60%.
Solution 2
To solve this problem, we first need to understand the Punnett square for this cross.
When two heterozygous animals (Ll x Ll) are crossed, the Punnett square would look like this:
L l
L LL Ll
l Ll ll
From this, we can see that the genotypic ratio is 1 LL : 2 Ll : 1 ll.
However, we are told that the trait for long necks is an autosomal dominant trait with 80% penetrance. This means that not all animals with the dominant allele will express the trait.
So, we need to calculate the probability of the offspring having long necks, taking into account the 80% penetrance.
The probability of an offspring being LL is 1/4, and since LL will definitely have a long neck, we can say that the probability of an offspring being LL and having a long neck is 1/4.
The probability of an offspring being Ll is 1/2. However, since the penetrance is 80%, only 80% of these Ll offspring will have long necks. So, the probability of an offspring being Ll and having a long neck is 1/2 * 0.8 = 0.4.
Adding these probabilities together, the total probability of an offspring having a long neck is 1/4 (for LL) + 0.4 (for Ll) = 0.65, or 65%.
So, none of the provided answer choices are correct. The correct answer should be 65%.
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