1. Decide if each of the following situations fits the binomial setting. Give reasons for your answer in each case. If x has a binomial distribution, state the values of n and p.

a. Roll a fair die until it comes up six. Let x be the number of rolls needed to get the six.

b. Roughly 60% of Americans believe that extraterrestrial life exists on other planets. A random
sample of 10 Americans is selected and during phone interviews are asked their opinion on
extraterrestrial life. Let x be the number who say they believe in extraterrestrial life.

c. A deck of cards is shuffled. You draw a card and check to see if it is a red card and then
put it aside. Then you draw a second card and check to see if it is a red card and put it on top
of the first card drawn. You continue until you have drawn 5 cards. Let x be the number of red
cards in the five that were drawn.

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