Question

sum of drawing a marble, noting the color, replacing the marble in the bag, and then drawing a second marble and noting the color before returning it to the bag. the point scheme for the game is detailed in the table below. point values for marble game black marble points red marble points both black: +2 points both red: +4 points different colors: -1 point different colors: -1 point both red: 0 points both black: 0 points if seth is challenged to a game by a classmate, which statement below is correct in all aspects in helping him make the correct choice? since e(black) = 0.24 and e(red) = 0.16, seth should choose to play black marbles. e(red) will be twice that of e(black), so seth should choose to play red marbles. since e(red) = e(black), it is a fair game, so it doesnt matter which color seth chooses. both options will lose points because there are two ways to lose points and only one way to gain points. he should choose neither color.

Explanation:

Step1: Recall expected - value concept

Expected value (E) helps in decision - making for games. Higher E indicates a more favorable choice.

Step2: Analyze given expected values

We are given that \(E(\text{black}) = 0.24\) and \(E(\text{red})=0.16\). Since \(0.24>0.16\), the expected value of playing black marbles is higher.

Answer:

Since \(E(\text{black}) = 0.24\) and \(E(\text{red}) = 0.16\), Seth should choose to play black marbles.