Nose bleeds in young children is fairly common, especially in summers. The front part of the nostrils is soft and wet and has got a rich supply of blood. This areas is also predisposed to crusting owing to breathing in hot and dry air. Any trauma to this part could lead to profuse bleeding. Children usually pick their nose and end up with nose bleeds. If you child is otherwise well, then this is the most plausible reason. You need to make sure that nose is kept moist. Use over the counter saline nasal drops liberally to prevent nasal dryness. However, it would be prudent to consult a paediatrician to make sure there is no concomittent illness that needs treatment.