Questions: Homework: Section 4.3 Score: 4/9 Answered: 4 / 9 Question 5 A binomial experiment consists of 10 trials. The probability of success on trial 3 is 0.88. What is the probability of failure on trial 7? 0.58 0.19 0.63 0.12 0.68 0.23 Submit Question

Homework: Section 4.3 Score: 4/9 Answered: 4 / 9 Question 5 A binomial experiment consists of 10 trials. The probability of success on trial 3 is 0.88. What is the probability of failure on trial 7? 0.58 0.19 0.63 0.12 0.68 0.23 Submit Question
Transcript text: Homework: Section 4.3 Score: 4/9 Answered: $4 / 9$ Question 5 A binomial experiment consists of 10 trials. The probability of success on trial 3 is 0.88 . What is the probability of failure on trial 7 ? 0.58 0.19 0.63 0.12 0.68 0.23 Submit Question
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Solution

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Solution Steps

Step 1: Understand the Nature of a Binomial Experiment

A binomial experiment is characterized by a fixed number of independent trials, each with two possible outcomes (success or failure), and the probability of success is constant across all trials.

Step 2: Calculate the Probability of Failure

Given the probability of success \(p = 0.88\) in any trial, the probability of failure \(q\) in any trial is simply \(1 - p\), which equals \(q = 0.12\).

Step 3: Apply the Probability of Failure to the Specified Trial

Since the probability of success (and thus failure) is constant across all trials in a binomial experiment, the probability of failure in the specified trial \(m = 7\) is the same as in any other trial, which is \(q = 0.12\).

Final Answer:

The probability of failure in trial \(m = 7\) of the binomial experiment, rounded to 2 decimal places, is 0.12.

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