You actually got it backwards, we are talking about the failure rate not the success rate. ( the succes rate is 2/3 so he would want it to change to 4/5 like you said.)
1/3 fail rates means that if you detonate the bomb 3 times 1 of those times it will fail.
1/5 is if you detonate it 5 times 1 of those times it will fail
meaning 1/5 gives you more chances of it not failing