At Guadalajara airport in Mexico, passengers must claim their luggage and then proceed to customs. In the customs area, each passenger will press a button that activated a modified stoplight. This light has only red and green bulbs. If the green light shows, the passenger is free to go. If the light turns red, then the customs agent will inspect the passenger’s luggage. Customs officials claim that the light has probability of 0.30 of showing red on any press of the button. Find the probability that more than two of the family members in front of you are stopped.

For every corresponding pair of cross sections, the area of the cross section of a sphere with radius r is equal to the area of the cross section of a cylinder with radius and height 2r minus the volume of two cones, each with a radius and height of r. a cross section of the sphere is and a cross section of the cylinder minus the cones, taken parallel to the base of cylinder, is the volume of the cylinder with radius r and height 2r is and the volume of each cone with radius r and height r is 1/3 pie r^3. so the volume of the cylinder minus the two cones is therefore, the volume of the cylinder is 4/3pie r^3 by cavalieri's principle. (fill in options are: r/2- r- 2r- an annulus- a circle -1/3pier^3- 2/3pier^3- 4/3pier^3- 5/3pier^3- 2pier^3- 4pier^3)