A Pair of Fair Dice Is Tossed $A ^ { c }$

question 152

Essay

A pair of fair dice is tossed. Events A and B are defined as follows. A: {The two numbers rolled are different} B: {At least one of the numbers is greater than 2} a. Identify the sample points in the event $A ^ { c }$ .
b. Identify the sample points in the event $B ^c$ .
c. Identify the sample points in the event $A ^ { c } \cup B ^c$ .
d. Identify the sample points in the event $A ^ { c } \cap B^ c$ .
e. Find $P \left( A ^ { c } \cup B ^ { c } \right)$ .
f. Find $P \left( A ^ { c } \cap B ^ { c } \right)$ .

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Definitions:

Maximize Profits

A strategy or goal where a firm or individual seeks to achieve the highest possible profit from its operations.

Peak Efficiency

The state of operation in which a system or process achieves its maximum output with the lowest input, often ideal in terms of productivity.

Perfectly Competitive Firm

A company that operates in a market where there are many sellers and buyers, the product is homogeneous, and there is free entry and exit from the market.

MR (Marginal Revenue)

The surplus income obtained by selling an extra unit of a product or service.