Well, they say asthma isn't hereditary, but there apparently is a link. My source says that if one parent has asthma then the chances rise from about 10 percent (standard percentage if neither parent has asthma) to 25 percent.

As for allergies, chances are around 35-65 percent.

But I only checked one source and they did say percentages varied quite a bit (It was an organization website so I figured they did their homework on the matter before posting the information), and it did not specify what age symptoms would appear.

You can help your baby out by keeping a clean house, washing blankets and pillowcases every ten days, and not smoking.
Source for more information on prevention.