If James only missed one question in all five rounds of five questions, he correctly answered 5 * 5 - 1 = <<5*5-1=24>>24 questions
Before the bonus, James earned 24 correct answers * 2 points/answer = <<24*2=48>>48 points.
Since missing one question would only disqualify him from receiving a bonus in one round, he would earn a bonus for 5-1=<<5-1=4>>4 rounds.
He should expect a bonus of 4 rounds* 4 points/round= <<4*4=16>>16 points.
Including his bonus, James scored a total of 48 + 16 = <<48+16=64>>64 points.
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