From 10 men and 8 women in a pool of potential jurors, 12 people are chosen at random to constitute a jury. suppose that you observe the number of men who are chose for the jury. let a be the event that at least half of the 12 jurors are men and b be the event that at least half of the 8 women are on the jury.

(a) determine the sample space of this random experiment.

(b) find a b, a b, and a b? listing the outcomes for each of those three events.

(c) are a and b mutually exclusive? (explain your answer) (d) are a and b? mutually exclusive? (explain your answer)

(e) are a? and b? mutually exclusive? (explain your answer)

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

Idon’t know how to do that