The rituals such as these are designed to eliminate the basic and primary fear from our mind at first place and as a start and motivation towards living good life.
Since their are many ways prescribed in ancient texts to wash away sins, bad karma ,negative thoughts etc. Like Chanting shlokas ,listining to puranas ,total devotion
etc.Those who cant do such things in practical life, has a easy way out to wash away sins,bad karmas by these rituals. its soul purpose is to free the mind from bondage
of these thoughts and burden. Another purpose of performing such rituals is to motivate us to go to pilgrimage and to expand our knowledge obout this world. In my Experience
,when we go to pligrimage apart from expanding our world it serves to ease out our fear about our actions ,sins and motivates us to act good.
Bad sins can not be washed away from us unless we are out of fear about them. since the perception about our sins, negative thoughts ,bad karmas resides in our mind we wont be
able to get rid from them completely. Our mind and consciousness always reminds us about that. So by doing Counterbalancing acts to these we can get rid of fear of sin ,bad karma from our mind
and replacing these fears with confidence ,only by acting in right way. Like helping others , understanding others ,following ones dharma, respecting every one including nature etc.
Yes its definitely possible to wash away or sins,bad karma ,negative thoughts etc. by acting just right and balancing our bad deeds with good ones.And to make ourselves free from bondage of fear of sins.
Please refer http://www.hinduism.co.za/sinner.htm for more.