**Express the indicated degree of likelihood as a probability value between 0 and 1. Use only decimals.**


In one of New York State’s instant lottery games, the chances of a win are stated as “4 in 21.”


The probability is approximately 

To express the indicated degree of likelihood as a probability value between 0 and 1, we can interpret "4 in 21" as a ratio of the number of favorable outcomes to the total number of outcomes.

The probability \( P \) can be calculated as:

\[
P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{4}{21}
\]

Now, calculate the decimal value:

\[
P \approx \frac{4}{21} \approx 0.1905
\]

So, the probability is approximately **0.1905**.

Would you like any details on this calculation or have any questions?

Here are 5 related questions to expand on this concept:

1. How would the probability change if the chances were "6 in 21" instead of "4 in 21"?
2. What is the probability of not winning in this lottery game?
3. If the chances were "4 in 25," what would the probability be?
4. How would you express a probability of 0.25 as a "X in Y" ratio?
5. What is the probability of winning at least once if you play the lottery game 3 times?

**Tip:** When calculating probabilities, always ensure that the total number of outcomes includes all possible scenarios, including both favorable and unfavorable outcomes.

Understand how to express the likelihood as a probability value between 0 and 1 using the ratio "4 in 21". Learn the calculation process and obtain the approximate decimal probability. Suitable for advanced high school students.

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