Can my marriage survive after wife admits to cheating?

Me and my wife have been married for over 3 years and we have a 1 year old son. We're both 25 years old. We had been dating for 6 years before we got married. We're were both happily married and our sex life was amazing and never got boring for either of us. Recently on a night out, she cheated on me while she was drunk. A guy I know saw her at the club dancing with a guy and recorded her with him and he said he saw her leave with him. I asked her if she cheated and at first she denied it, but later admitted it was true. She admitted it without me telling her how I knew. She says she'll never betray me again and she was begging me for another chance. Normally I'd be out the door and she'd never see me again, but this is different, we have a child. With divorces, it's almost impossible for the guy to come out feeling justice. Divorce favours women in almost every single way, even when it's clearly the woman's fault. I don't want my child to grow up in a broken home. Is there any way me and my wife can fix our marriage. She's suggested couple's therapy, but I'm one of those guys whose always seen therapy as a money making scam. But I'm open to it, if it will save our marriage.
Can my marriage survive after wife admits to cheating?
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