Whoops messed up the letters. And too lazy to correct it. So letter A is Chuck and letter C is Alan
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One rule: They always shoot the guy with the highest percentage of making the shot.
ABC:
A survives: A hits, B misses, A hits; A hits, B misses, A misses, B misses; A misses, (doesn't matter), A hits = 0.5*0.2*0.5 + 0.5*0.2*0.5*0.2+0.5*0.5 = 31%
B survives: A hits, B hits; A hits, B misses, A misses, B hits; A misses, B hits, A misses = 0.5*0.8 + 0.5*0.2*0.5*0.8+ 0.5*0.8*0.5 = 64%
C survives: A misses, B misses, A misses = 0.5*0.2*0.5 = 5%
ACB:
A survives: A hits, B misses, A hits; A hits, B misses, A misses, B misses; A misses, A hits = 0.5*0.2*0.5 + 0.5*0.2*0.5*0.2 + 0.5*0.5 = 31%
B survives: A hits, B hits; A hits, B misses, A misses, B hits = 0.5*0.8 + 0.5*0.2*0.5*0.8 = 44%
C survives: A misses, A misses = 0.5*0.5 = 25%
BAC:
A survives: B hits, A hits; B hits, A misses, B misses, A hits; B misses, A hits, B misses; B misses, A misses, A hits 0.8*0.5 + 0.8*0.5*0.2*0.5 + 0.2*0.5*0.2 + 0.2 * 0.5 * 0.5 = 51%
B survives: B hits, A misses, B hits; B hits, A misses, B misses, A misses; B misses, A hits, B hits 0.8*0.5*0.8 + 0.8*0.5*0.2*0.5 + 0.2*0.5*0.8 = 44%
C survives: B misses, A misses, A misses = 0.2*0.5*0.5 = 5%
BCA:
A survives: B hits, A hits; B hits, A misses, B misses, A hits; B misses, A hits 0.8 * 0.5 + 0.8*0.5*0.2*0.5+0.2*0.5 = 54%
B survives: B hits, A misses, B hits; B hits, A misses, B misses, A misses= 0.8 * 0.5 * 0.8 + 0.8*0.5*0.2*0.5 = 0.32 + 0.04 = 36%
C survives: B misses, A misses = 0.2 * 0.5 = 10%
CAB:
A survives: A hits = 50%
B survives: not possible = 0%
C survives: A misses = 50%
CBA:
A survives: A hits = 50%
B survives: not possible = 0%
C survives: A misses = 50%
A(Chuck) = (31 + 31 + 51 + 54 + 50 + 50)/6 = 267/6 = 44.5%
B(Bob) = (64 + 44 + 44 + 36 + 0 + 0)/6 = 188/6 = 31.33%
C(Alan) = ( 5 + 25 + 5 + 10 + 50 + 50)/6 = 145/6 = 24.17%