i개의 부분적 지식으로부터 맞힐 확률 | (a) s = ⌊log2k⌋ ( m s ) p r s ( 1 − p r ) m − s · ( 2 · f ( k , s ) − f ( 2 s , s ) ) | (a) 0 ≤ i < s = ⌊log2k⌋ ∑ i = 0 s − 1 ( m i ) p r i ( 1 − p r ) m − i · f ( k , i ) |
(b) s = ⌊log2k⌋ <i ≤ m ∑ i = s + 1 m ( m i ) p r i ( 1 − p r ) m − i · f ( k , i ) | (b) s = ⌊log2k⌋ ( m s ) p r s ( 1 − p r ) m − s · ( f ( 2 s , s ) − f ( k , s ) ) |
정답을 맞힐 확률 | ( m s ) p r s ( 1 − p r ) m − s · ( 2 · f ( k , s ) − f ( 2 s , s ) ) + ∑ i = s + 1 m ( m i ) p r i ( 1 − p r ) m − i · f ( k , i ) | ∑ i = 0 s − 1 ( m i ) p r i ( 1 − p r ) m − i · f ( k , i ) + ( m s ) p r s ( 1 − p r ) m − s · ( f ( 2 s , s ) − f ( k , s ) ) |
문항 난이도 | ∑ i = 0 m ( m i ) p r i ( 1 − p r ) m − i · f ( k , i ) |