What is the mode of inheritance?

[Dmitriy93]

In humans, there is a genetic disease called Hypophosphatemia that causes rickets. Here is a list of the phenotypes of the parents and their offspring from four different marriages.

Marriage #1:
Mother phenotype: Healthy
Father phenotype: Rickets

Offspring phenotype:
Females: rickets
Males: healthy

Marriage #2:
Mother phenotype: Rickets
Father phenotype: Healthy

Offspring phenotype:
Females: 50% rickets, 50% healthy
Males: 50% rickets, 50% healthy

Marriage #3:
Mother phenotype: Rickets
Father phenotype: Healthy

Offspring phenotype:
Females: rickets
Males: rickets

Marriage #4:
Mother phenotype: Healthy
Father phenotype: Healthy

Offspring phenotype:
Females: healthy
Males: healthy

Question: What is the inheritence mode of the disease?
Note: In the question, there's no mention of the married couples being related to each other in any way, so I'm assuming these couples are not relatives.

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My conclusion considering the given data is that the inhertence mode of the disease is autosmal recessive. If it were dominant (either autosomal or x-linked), the disease would've been somehow expressed in marriage #4. It doesn't seem to be x-linked recessive, looking at marriage #2.

If it were X-linked recessive, for 50% of their offspring to be sick in marriage #2, the father would have to carry a recessive mutant gene as well. If he were carrying a recessive mutant gene, he would have been sick, yet he's healthy. For 50% of the offspring to be healthy (as showed), there would need to be a dominant gene preventing the mutant recessive gene from being expressed.

I'm just trying to figure out whether my way of going about solving this question is correct or not...