Question

Soldiers must successfully pass PMI&E between T-6 and T-week prior to firing any live ammunition by receiving all GOs on demonstrated performance and achieving a passing score of 80 percent or higher on a written test?

a-true
b-false

Answer 1

The probability of the student passing a 10-question true-false quiz by guessing is calculated using the binomial probability formula. It requires summing the probabilities of getting at least 7, 8, 9, or 10 questions correct. Each scenario's probability must be computed separately and then added together.

Step-by-step explanation:

To calculate the probability of a student passing a 10-question true-false quiz by guessing, we first need to establish the criteria for passing. In this case, getting at least 70 percent, which means answering at least 7 out of 10 questions correctly.

Because each question can only be true or false, there is a 1/2 chance of guessing each question correctly. To find the probability of guessing exactly 7 questions right, we use the binomial probability formula, which for a single value 'k' (number of successes in trials) is given by P(X = k) = (n choose k) · (p)^k · (1-p)^(n-k), where 'n' is the number of trials, 'p' is the probability of success on a single trial, and '1-p' is the probability of failure.

To calculate the total probability of passing the quiz, we must consider all the scenarios in which the student can pass, i.e., guessing 7, 8, 9, or all 10 correctly. We must sum the probabilities of all these separate events:

1. Probability of exactly 7 correct guesses.
2. Probability of exactly 8 correct guesses.
3. Probability of exactly 9 correct guesses.
4. Probability of getting all 10 correct.

By calculating each of these probabilities and summing them, we determine the overall probability of passing the quiz.