Answer:
3/64 B- vv dd
Step-by-step explanation:
We know that the alleles for all of the three traits assort independently. So we can think about them separately.
Coat color:
Let us say that the dominant allele coding for Black is B while the recessive allele coding for chocolate is b.
Parentals) Bb x Bb
F1) 1/4 BB, 2/4 Bb, 1/4 bb
Vision:
Let us say that the dominant allele coding for normal vision is N while the recessive allele coding for PRA is n.
Parentals) Nn x Nn
F1) 1/4 NN, 2/4 Nn, 1/4 nn
Hip joint
Let us say that the dominant allele coding for the normal hip joint is D while the recessive allele coding for dysplasia is d.
Parentals) Dd x Dd
F1) 1/4 DD, 2/4 Dd, 1/4 dd
Now, we need to know the chance that the first pup born to these dogs will be black, have PRA, and have hip dysplasia. The genotype of this individual would be B- nn dd, where the symbol - represents the dominant and/or the recessive allele.
Black coat = 1/4 BB + 2/4 Bb = 3/4 B-
PRA = 1/4 nn
Dysplasia = 1/4 dd
The probability of getting the first individual with these genotypes results from their multiplication.
3/4 B- x 1/4 vv x 1/4 dd = 3/64 B- vv dd
The product probability rule allows us to calculate the probability of occurrence of event A and event B at the same time. It is about a joint probability of two or more events that might happen simultaneously, not excluding each other. This rule is based on the dependence or independence of the events. Two events A and B are independent of each other if one of them does not affect the occurrence of the other one. For independent events, the rule establishes that, given two different events A and B, the probability of occurrence of both together is
P(A∩B) = P(A) x P(B)