Probability of Getting All Six Questions Correct

E

This is binomial distribution with p = 0.5, q = 0.5, n = 6, r = 6. Therefore 6!(0.5^6)(0.5^0)/6!0! = 0.0156.

To solve this problem, let's analyze the probability of getting a single question correct through guessing.

For each question, there are two possible outcomes: getting it right or getting it wrong. Since the test consists of true-false questions, the probability of guessing the correct answer for each question is 1/2 (or 0.5), and the probability of guessing the wrong answer is also 1/2.

Since the test has six questions and you're guessing the answers to all of them, the probability of getting all six questions correct would be the product of the probabilities of getting each individual question correct.

Mathematically, this can be calculated as follows:

Probability of getting all six questions correct = (Probability of getting one question correct)^6

Therefore, the probability is (1/2)^6, which simplifies to 1/64.

To convert this fraction to a decimal, we divide 1 by 64:

Probability = 1/64 = 0.015625

Therefore, the correct answer is E. 0.0156.

Note: The answer choices provided in the question are slightly rounded. The exact decimal value is 0.015625, but the closest rounded value is 0.0156, which corresponds to option E.