Questions: In a certain instant lottery game, the chances of a win are stated as "7 in 16." Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive. The probability is (Round to three decimal places as needed.)

In a certain instant lottery game, the chances of a win are stated as "7 in 16." Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive. The probability is (Round to three decimal places as needed.)
Transcript text: In a certain instant lottery game, the chances of a win are stated as "7 in 16." Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive. The probability is $\square$ (Round to three decimal places as needed.)
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Solution

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Solution Steps

Step 1: Identify the Winning and Total Outcomes

Given that there are 7 winning outcomes and a total of 16 possible outcomes, we can proceed to calculate the probability of winning.

Step 2: Calculate the Probability

The probability of winning is calculated using the formula $\frac{x}{y}$, which gives us $\frac{7}{16} = 0.438$.

Step 3: Express as a Decimal

The division operation inherently expresses the result as a decimal. Therefore, the probability as a decimal is 0.438.

Step 4: Rounding

After rounding to 3 decimal places, the probability is 0.438.

Step 5: Validation

The calculated probability is within the valid range of 0 to 1 inclusive.

Final Answer: The probability of winning the lottery game, rounded to 3 decimal places, is 0.438.

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