Hi, I am playing wuropean (single zero) rouellte. I am betting on the same 2 dozens every spin, so am covery 24 out of 37 of the board. What are teh odds of me losing 8 spins in a row betting on the same 2 dozens every spin?

In European roulette, there are 37 numbers (1-36 plus a single zero). When betting on 2 dozens, you're covering 24 numbers out of the 37, which means the probability of losing a single spin is the chance that the ball lands on one of the 13 numbers (12 not covered by your dozens and the single zero).

The probability of losing a single spin is:

\[
P(\text{Loss in one spin}) = \frac{13}{37}
\]

Now, to find the probability of losing 8 spins in a row, you raise this single-spin loss probability to the power of 8:

\[
P(\text{Lose 8 spins in a row}) = \left(\frac{13}{37}\right)^8
\]

Let's calculate this probability.

The probability of losing 8 spins in a row, while betting on the same 2 dozens in European roulette, is approximately 0.00023, or 0.023%. This is a very low probability.

Would you like more details or have any other questions?

Here are 5 related questions to expand on this:

1. What are the odds of losing 5 spins in a row?
2. How does the probability change if you bet on 1 dozen instead of 2?
3. What is the expected number of losses over 100 spins?
4. What are the chances of winning at least once within 8 spins?
5. How does European roulette compare to American roulette in terms of probabilities?

**Tip:** Understanding the probabilities helps you make informed decisions, but keep in mind that roulette outcomes are always independent, and past losses or wins don't influence future results.

Hi, I am playing European (single zero) roulette. I am betting on the same 2 dozens every spin, so am covering 24 out of 37 of the board. What are the odds of me losing 8 spins in a row betting on the same 2 dozens every spin?

Find out the probability of losing 8 consecutive spins in European roulette while betting on 2 dozens. This problem involves key concepts from probability theory, using the law of independent events to determine the likelihood of this rare event, suitable for Grades 9-12.

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