Lab tests of a new drug indicate a 70% success rate in completely curing the targeted disease. The doctors at the lab created the random data in the table using a representative simulation. The letter E stands for "effective," and N stands for "not effective." NEEE EEEN NEEN

NEEE EENE NNNE NEEN EENE

NENE NNNE ENEE

NEEN ENEE EENN ENNE NEEE

ENEN EEEN NEEE EENN

EENE EEEN EENE

ENEE ENNN EENE EEEN

NEEE ENEE NEEE

NENN EENN

ENNN NENN NEEN ENEE EENE

The estimated probability that it will take at least five patients to find one patient on whom the medicine would not be effective is .

The estimated probability that the medicine will be effective on exactly three out of four randomly selected patients is .

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)