Log In Start studying!

Select your language

Suggested languages for you:

Americas

English (US)

Europe

Q7E

Expert-verified

Discrete Mathematics and its Applications

Found in: Page 492

Book edition 7th

Author(s) Kenneth H. Rosen

Pages 808 pages

ISBN 9780073383095

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later

Short Answer

Question: The final exam of a discrete mathematics course consists of \(50\) true/false questions, each worth two points, and\(25\)multiple-choice questions, each worth four points. The probability that Linda answers a true/false question correctly is \(0.9\), and the probability that she answers a multiple-choice question correctly is \(0.8\). What is her expected score on the final?

Answer:

The expected score of Linda on the final is\(170\).

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information

The final exam of a discrete mathematics course consists of \(50\) true/false questions, each worth two points, and \(25\)multiple-choice questions, each worth four points.

The probability that Linda answers a true/false question correctly is\(0.9\), and the probability that she answers a multiple-choice question correctly is\(0.8\).

Step 2: Theorem for expected number of successes

The expected number of successes when n mutually independent Bernoulli trials are performed, where \(p\) is the probability of success on each trial, is\(np\).

Formula used:

\(E(X + Y) = E(X) + E(Y)\)

Step 3: Calculate the expected value

Let X be the random variable giving the score on the true-false questions and let Y be the random variable giving the score on the multiple-choice questions.

The expected number of true-false questions Linda gets right is the expectation of the number of successes when\(50\)Bernoulli trials are performed with\(p = 0.9\) \(p = 0.9\)

By given theorem, the expectation for the number of successes is np is \(50*0.9 = {\rm{ }}45\)

Since each problem counts \(2\)points, the expectation of\(X\)is \(45*2 = 90\)

Similarly, the expected number of MCQs she gets right is the expectation of the number of successes when \(25\) Bernoulli trials performed \(\left( {p is 0.8} \right), i.e., 25*0.8 = 20\)

Since each problem counts four point, the expectation of Y is \(20*4 = 80\)

Therefore, the expected score on the exam is

\(\begin{array}{l}E(X + Y) = E(X) + E(Y)\\ = 90 + 80\\ + 170\end{array}\)

The expected score of Linda is \(170\).

Most popular questions for Math Textbooks

Question: What is the probability that a positive integer not exceeding $100$ selected at random is divisible by $5 or 7$ ?

Question 2. To determine

What is the probability that two people chosen at random were born during the same day of the week?
What is the probability that in group of $n$ people chosen at random there are at least two born in the same day of the week?
How many people chosen in random are needed to make the probability greater than $\frac{1}{2}$ that there are at least two people born in the same day of the week?

Question: Suppose that the probability that \(x\) is in a list of n distinct integers is\(\frac{2}{3}\) and that it is equally likely that \(x\) equals any element in the list. Find the average number of comparisons used by the linear search algorithm to find \(x\) or to determine that it is not in the list.

Question: Suppose that 100 people enter a contest and that different winners are selected at random for first, second, and third prizes. What is the probability that Michelle wins one of these prizes if she is one of the contestants?

Question 2. To show

If events $E$ and $F$ are independent, then events $\bar{E}$ and $\bar{F}$ are also independent.

Want to see more solutions like these?

Sign up for free to discover our expert answers

Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free