Atrue-false test consists of six questions. if you guess the answer to each question, what is the probability of getting all six questions correct?

The probability of getting all six questions correct is .

Further Explanation:

Probability can be defined as the ratio of favorable number of outcomes to the total number of outcomes.

Given:

There are true-false questions in an exam. A student answers all questions by guess.

Concept used:

The probability of any event can be calculated as,

Here, is the total number of elements in event and is the number of element in sample space of an experiment.

Calculation:

The sample space is the total possible outcomes in an experiment.

Consider as the number of element in sample space .

The possible outcomes in sample space are either true or false.

Therefore, the number of element in sample space is,

Consider as the event that the answer of first question is true, as the number of ways that the answer of first question is true and as the probability of event .

The number of ways that the answer of first question is true can be calculated as,

To obtain the probability , replace by in the equation as,

Substitute for and for in the equation to obtain the probability  .

Now, the probability that all six questions are correct can be obtained as,

The probability of getting all six questions correct is .

Learn more:

1. Learn more about unit conversion

2. Learn more about non-collinear

3. Learn more about inverse of function

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Probability

Keywords: Probability, outcome, total number of outcomes, ratio, favorable number of outcomes, six, six questions, correct, false, true, guess, consist, test, answer.