Combinatoric Juggle Analysis

HOLY FUCK

[X] [O] [O] [O]

P(hitting target on first try) = 1/4

FOUR SCENARIOS

#1: We assume the first knife missed and did not die to the knife
P(knife missing) = 3/4
P(knife hitting)   = 1/4

A = P(hitting first and missing second) = 1/4 * 3/4 = 3/16
B = p(missing first and hitting second) = 3/4 * 1/4 = 3/16
C = p(missing both)                           = 3/4 * 3/4 = 9/16
D = p(hitting both)                             = 1/4 * 1/4 = 1/16

3 + 3 + 9 + 1 = 16/16 (Good, we covered all scenarios for the two juggles)

P(at least one knife hitting) = A + B + D = 3/16 + 3/16 + 1/16 = 7/16 ~ 43.75%