Suppose there is a 51% chance of rain for each of the next four days.  The probability that it rains every day for the next four days is .514. Express this as a decimal and round your answer to four decimal places.

To find the probability that it rains every day for the next four days, given that there is a 51% chance of rain each day, we need to calculate the probability that it rains on all four days. 

Given that the probability of rain on each day is \( 0.51 \), the probability that it rains on all four days is:

\[
0.51 \times 0.51 \times 0.51 \times 0.51 = 0.51^4
\]

Let's calculate this value.

\[
0.51^4 = 0.06769551
\]

Rounding this to four decimal places:

\[
\text{Probability} = 0.0677
\]

So, the probability that it rains every day for the next four days, rounded to four decimal places, is **0.0677**.

Would you like more details, or do you have any other questions?

Here are five related questions:

1. What is the probability that it rains on exactly three out of the four days?
2. How does the probability change if the chance of rain increases to 60% each day?
3. What is the probability that it does not rain at all over the four days?
4. How would you calculate the probability of rain on at least one of the four days?
5. How would the result change if the number of days increased to five with the same probability of rain each day?

**Tip:** For compound probability problems, multiplying the individual probabilities gives the probability of all events occurring together.

Understand how to calculate the probability that it rains every day for the next four days, given a 51% chance of rain each day. Explore the mathematical process using probability theory and independent events. Suitable for students and enthusiasts of probability mathematics.

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