Consider the Following Scenario to Answer the Questions That Follow

question 77

Multiple Choice

Consider the following scenario to answer the questions that follow.
Suppose that in an experimental setting, 100 students are asked to choose between Gamble A and Gamble B, where:
Gamble A: The student will receive $50 with a 70% probability and $100 with a 30% probability.
Gamble B: The student will receive $50 with a 50% probability, $200 with a 25% probability, and $0 (nothing) with a 25% probability.
-Which of the following formulas shows the correct formula for the expected value (EV) of Gamble B?

• A) EV = 0.5 × ($50) + 0.25 × ($25)
• B) EV = 0.5 × ($50) + 0.25 × ($100) + 0.25 × ($250)
• C) EV = 0.5 × ($50) + 0.5 × ($200)
• D) EV = 0.5 × ($50) + 0.25 × ($200)
• E) EV = 0.25 × ($50) + 0.25 × ($200)

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Definitions:

Welded Tuffs

Volcanic deposits formed from hot ash flows that solidify, with the particles welding together due to the heat.

Andesite

A volcanic rock of intermediate composition, typically found in volcanic arcs associated with subduction zones, characterized by a medium gray or brown color.

Silica Content

The proportion of silicon dioxide (SiO2) in a rock, mineral, or geological sample, influencing its physical properties and behavior.

Caldera

A vast volcanic depression, usually created when land collapses after a volcanic explosion.