When playing roulette at a casino, a gambler is trying to decide whether to bet $5 on the number 33 or to bet $5 that the outcome is any one of the three possibilities 00 comma 0 comma or 1. The gambler knows that the expected value of the $5 bet for a single number is negative 0.53 cents. For the $5 bet that the outcome is 00 comma 0 comma or 1, there is a probability of StartFraction 3 Over 38 EndFraction of making a net profit of $20 and a StartFraction 35 Over 38 EndFraction probability of losing $5. a. Find the expected value for the $5 bet that the outcome is 00 comma 0 comma or 1. b. Which bet is better: a $5 bet on the number 33 or a $5 bet that the outcome is any one of the numbers 00 comma 0 comma or 1? Why?

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