An Experiment Consists of Casting a Pair of Dice and Observing

question 7

Multiple Choice

An experiment consists of casting a pair of dice and observing the number that falls uppermost on each die. We may represent each outcome of the experiment by an ordered pair of numbers, the first representing the number that appears uppermost on the first die and the second representing the number that appears uppermost on the second die. Consider the sample space S = {(1, 1) , (1, 2) , (1, 3) , (1, 4) , (1, 5) , (1, 6) ,
(2, 1) , (2, 2) , (2, 3) , (2, 4) , (2, 5) , (2, 6) ,
(3, 1) , (3, 2) , (3, 3) , (3, 4) , (3, 5) , (3, 6) ,
(4, 1) , (4, 2) , (4, 3) , (4, 4) , (4, 5) , (4, 6) ,
(5, 1) , (5, 2) , (5, 3) , (5, 4) , (5, 5) , (5, 6) ,
(6, 1) , (6, 2) , (6, 3) , (6, 4) , (6, 5) , (6, 6) }
Determine the event that the sum of the numbers falling uppermost is greater than or equal to 7.

• A) {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}
• B) {(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 5), (4, 6), (5, 6)}
• C) {(1, 6), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 3), (4, 5), (4, 6), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
• D) Ø

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Definitions:

Equal Marginal Principle

Principle that utility is maximized when the consumer has equalized the marginal utility per dollar of expenditure across all goods.

Hicksian Substitution Effect

Alternative to the Slutsky equation for decomposing price changes without recourse to indifference curves.

Indifference Curves

A graph showing different bundles of goods between which a consumer is indifferent.

Lagrangian

Function to be maximized or minimized, plus a variable (the Lagrange multiplier) multiplied by the constraint.