Jairus was the ruler of the synagogue. It is easy to forget how antagonistic religious leaders were to Jesus. This is a bold and desperate concession on his part.
Don't know how I'd missed this before but the woman had been suffering for 12 years and the girl who died was 12 years old.
After they heard the girl was dead, Jesus told the man, "Don't fear, only believe." In the heat of that moment, when your precious daughter just died, that must have sounded ridiculous. I suspect those same words would have sounded even stranger and harder to the woman who'd suffered for a dozen years. Yet, Jesus healed both the acute and the chronic problem -- one in dramatic fashion, one without even looking.
The disciples' statement, "How can you say, 'someone touched you,' when there is a crowd pressing you on every side?" and Jesus' response to the woman tell me that many can be in close, close proximity to Jesus and still not have any experience of his power! God, don't let me be part of a crowd that hangs around Jesus but misses His power because of a lack of faith.