   Chapter 14.2, Problem 47E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# Guessing on a test An exam has ten true-false questions. A student who has not studied answers all ten questions by just guessing. Find the probability that the student correctly answers all ten questions.

To determine

To find:

The probability that the student correctly answers all ten questions.

Explanation

Given:

An exam has ten true-false questions. A student who has not studied answers all ten questions by just guessing.

Approach:

Combinations: Combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter.

Formula used:

Cnr=n!r!(nr)! ….…(1)

Here, n is the total number of items and r is the number of items being chosen at a time.

If E is the event in a sample space S, then the probability of E is

P(E)=Cnrprqnr(2)

Here, p is the probability of success, q is the probability of failure and n is the number of independent trials.

Calculation:

There are 10 true-false questions in a exam. So, there is equal possibility that answer is correct or not. Let the probability that answer is correct is p and probability that answer is incorrect is q. Student answered all the questions. Now,

n=10p=12q=12r=10

Substitute 10 for n and 10 for r in equation (1).

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