Dependent probability Captain Emily has a ship , the H . M . S Crimson Lynx . The ship is five furlongs from the dread pirate Umaira and her merciless band of thieves . of hitting the pirate ship . If her ship has been If her ship hasn ' t already been hit , Captain Emily has probability hit . Captain Emily will always miss . of hitting the Captain ' s ship . If her sho If her ship hasn ' t already been hit , dread pirate Umaima has probability has been hit , dread pirate Umaima will always miss . If the Captain and the pirate cach shoot once , and the pirate shoots first , what is the probability that the pirate misses the Captain ' s ship , but the Captain hits ?

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

A= the square root of 3“if letters are anything like people, they’re all equal and deserve to be treated equally.”