A binomial experiment consists of 11 trials. The probability of success on trial 4 is 0.26. What is the probability of failure on trial 8?

0.33
0.88
0.74
0.27
0.15
0.4

In a binomial experiment, each trial is independent of the others, and the probability of success remains the same across all trials. Therefore, the probability of success on any given trial will always be the same.

In this case, you are told that the probability of success on trial 4 is \(0.26\). This means the probability of success on any trial, including trial 8, is also \(0.26\).

The probability of failure on any given trial is:

\[
P(\text{failure}) = 1 - P(\text{success})
\]

Substituting the given probability of success:

\[
P(\text{failure}) = 1 - 0.26 = 0.74
\]

Thus, the probability of failure on trial 8 is \(0.74\), so the correct answer is:

\[
\boxed{0.74}
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. What is a binomial experiment, and what are its properties?
2. How do you calculate the probability of \(k\) successes in a binomial distribution?
3. Can the probability of success differ between trials in a binomial experiment?
4. How do you calculate the cumulative probability in binomial distributions?
5. What is the expected number of successes in 11 trials if the probability of success is 0.26?

**Tip:** In binomial experiments, understanding the independence of trials helps simplify many probability calculations.

A binomial experiment consists of 11 trials. The probability of success on trial 4 is 0.26. What is the probability of failure on trial 8?

Explore how to calculate the probability of failure in a binomial experiment with 11 trials, where the probability of success on trial 4 is 0.26. Learn about key concepts like independence of trials, binomial distribution, and how to use the formula P(failure) = 1 - P(success). Suitable for Grades 10-12 students.

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