At roulette, there are 38 slots. A "column" consists of 12 of these slots. A column pays 2 to 1. So, if you risk $1 on a column and win, you net gain +2 dollars. If you lose, your net equals –1 dollar. Suppose you will play for 100 rounds and bet one dollar on a column each round. (You may enter values rounded to the nearest cent. Beware of carried rounding error.) Your average net gain per play equals o.0526 dollars. The SD of your net gain per play equals 1.39 dollars. The expected value of your total net gain after 100 plays equals -5.3 dollars. The standard error of your total net gain after 100 plays equals 13.94 dollars.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
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Chapter1: Combinatorial Analysis
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At roulette, there are 38 slots. A "column" consists of 12 of these slots. A column pays 2 to 1. Thus, if you bet $1 on a column and win, you gain $2, whereas if you lose, you lose $1.

Consider a scenario where you play 100 rounds, betting $1 on a column each time. Here are the statistical outcomes:

- **Average Net Gain per Play**: $0.0526
- **Standard Deviation (SD) of Net Gain per Play**: $1.39
- **Expected Value of Total Net Gain after 100 Plays**: -$5.30
- **Standard Error of Total Net Gain after 100 Plays**: $13.94

The calculations show the expected monetary outcomes and variability when engaging in this betting strategy over multiple rounds.
Transcribed Image Text:At roulette, there are 38 slots. A "column" consists of 12 of these slots. A column pays 2 to 1. Thus, if you bet $1 on a column and win, you gain $2, whereas if you lose, you lose $1. Consider a scenario where you play 100 rounds, betting $1 on a column each time. Here are the statistical outcomes: - **Average Net Gain per Play**: $0.0526 - **Standard Deviation (SD) of Net Gain per Play**: $1.39 - **Expected Value of Total Net Gain after 100 Plays**: -$5.30 - **Standard Error of Total Net Gain after 100 Plays**: $13.94 The calculations show the expected monetary outcomes and variability when engaging in this betting strategy over multiple rounds.
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