I am 46 years old, and my period is 15 days late. how likely is it that i am pregnant? or is there something else that could be causing this?

Trust the test : Home pregnancy tests are very accurate. They are the same tests used in a doctors office. They can detect a pregnancy 7-10 days after conception. If you doubt the result you can repeat it in 1-2 days. If you were pregnant the hormone level would rise enough for detection. Cycle irregularity is not surprising at 40 years old. There are many options for cycle control.