The short answer is yes. To understand why, let's review how genes get passed down. (For more detailed information, you can read about genetic inheritance.)
You and your 4th cousin have the same 3rd great-grandparents. For you to have matching DNA with that cousin, the same section of DNA would have to be passed down through five generations to both of you. Since DNA recombination is a random process, it’s possible you won’t both inherit matching DNA, even though you share a common ancestor.
You can see an example of this process in the diagram below (Figure 1). The common ancestor couple (A) has three children together (B). Among these children, the DNA is randomly inherited (red and blue coloring). Several generations later, three cousins (C, D, and E) share different amounts of matching DNA. Two of the cousins (C and E) share no matching DNA.
Figure 1. An inheritance chart showing why you and some distant cousins may not be DNA matches.
Table 1 shows how likely you are to share DNA with a cousin. As you can see, you may have a known cousin—and perhaps a shared ancestor—but no DNA evidence to support your relationship.
| Relationship | Likelihood of a DNA Match |
|---|---|
| Siblings | 100% |
| 1st cousins | 100% |
| 2nd cousins | 100% |
| 3rd cousins | 98% |
| 4th cousins | 71% |
| 5th cousins | 32% |
| 6th cousins | 11% |
| 7th cousins | 3.2% |
| 8th cousins | 0.91% |
Table 1. The likelihood that you and a distant cousin have matching DNA.
Though the chances of sharing DNA with a cousin are lower the more distantly related you are to that cousin, there are still ways to find them through DNA. The simplest approach is to have more of your close family take a DNA test. The more of your close family members who are tested, the more likely it is that one of you will share matching DNA with that distant cousin.
The diagram below (Figure 2) shows how a close relative can share matching DNA with a distant cousin even when you do not. In the figure, the cousins (C, D, E, F, and G) are all descendants of a single couple (A). Person C does not share matching DNA with person G, who is a 3rd cousin. But their sibling, person D, does share matching DNA with G. Getting person D to take a test will let them and the rest of their family explore a whole new branch of their family tree.
Figure 2. An inheritance chart showing how a close relative may have a DNA match with a distant cousin when you do not.
Table 2 shows how likely it is that your close family members would have a DNA match with a cousin with whom you don't share DNA. Remember that if the cousin is on your father's side of the family, the close family member (like your brother or aunt) must also be on your father's side.
| Distant Relationship | Sibling | Uncle/Aunt | Niece/Nephew | Parent | Grandparent | First Cousin | Second Cousin |
|---|---|---|---|---|---|---|---|
| 3rd cousins | 87% | 99% | 64% | 96% | 100% | 94% | 97% |
| 4th cousins | 42% | 78% | 25% | 63% | 92% | 57% | 64% |
| 5th cousins | 15% | 37% | 8% | 26% | 58% | 22% | 26% |
| 6th cousins | 4% | 13% | 2% | 9% | 23% | 7% | 8% |
| 7th cousins | 1.5% | 4% | 0.8% | 3% | 8% | 2% | 3% |
| 8th cousins | 0.43% | 1.23% | 0.23% | 0.81% | 2.3% | 0.65% | 0.77% |
Table 2. The likelihood that a close relative on one side of your family has a DNA match with a distant cousin on the same side of the family, even if you don't have a DNA match.
It's important to remember that some of your close relatives, like your nephew or half-sister, have some ancestors that you don't share, which means their DNA matches along family lines that you don't share aren't relevant to you. On the other hand, if a close relative like your brother is a DNA match with someone, and you're not, you'll know that you're related to their match, too.