You are a contestant on a game show called “bargain or no bargain.” you are presented with three briefcases, which contain rewards of $500,000, $2,000, and $500. the host of the show says you can either open one random case and keep the amount inside, or you can accept a guaranteed award of $160,000. what is the mathematically correct decision, and why

a. take the $160,000, because it is greater than the expected value of the briefcases.
b. choose a briefcase, because the expected value is greater than $160,000.
c. choose a briefcase ,because the expected value is less than $160,00

Nthe opening scene of the movie raiders of the lost ark, indiana jones replaces a golden statue with a bag of sand. the platform on which the statue is placed is designed to detect the mass of the statue. if the bag of sand has a different mass than the statue, then a mechanism triggers and destruction ensues. the density of gold is about 20\text{ g/cm}^320 g/cm 3 20, space, g, slash, c, m, start superscript, 3, end superscript. the density of sand can be estimated at 2.5\text{ g/cm}^32.5 g/cm 3 2, point, 5, space, g, slash, c, m, start superscript, 3, end superscript. the gold statue can be modeled as a cylinder with height 25\text{ cm}25 cm25, space, c, m and radius 8\text{ cm}8 cm8, space, c, m. in terms of \piπpi, what is the mass of sand indiana jones needs to avoid triggering the mechanism?