부분적 지식 i개 중에 | (a) ‘옳은 답’ 하나와 ‘그른 답’ i-1개를 아는 경우(1 ≤ i ≤ k) ( k − 1 i − 1 ) / ( k i ) = i k | (b) k-1개의 ‘그른 답’을 아는 경우 ( k − 1 i ) / ( k i ) = 1 k | (c) i개의 ‘그른 답’을 아는 경우(0 ≤ i ≤ k-2) ( k − 1 i ) / ( k i ) = k − i k |
정답을 맞힐 확률 | ∑ i = 1 k ( k i ) p s i ( 1 − p s ) k − i ⋅ i k ⋅ 1 | ( k k − 1 ) p s k − 1 ( 1 − p s ) 1 ⋅ 1 k ⋅ 1 | ∑ i = 0 k − 2 ( k 2 ) p s i ( 1 − p s ) k − i ⋅ k − i k ⋅ 1 k − i |
∑ i = 1 k ( k i ) p s i ( 1 − p s ) k − i ⋅ i k + ( k k − 1 ) p s k − 1 ( 1 − p s ) 1 ⋅ 1 k | ∑ i = 0 k − 2 ( k i ) p s i ( 1 − p s ) k − i ⋅ 1 k |
문항 난이도 | ∑ i = 0 k − 1 ( k i ) p s i ( 1 − p s ) k − i ⋅ i + 1 k + p k |