/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 49 If you toss a fair coin six time... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 49

If you toss a fair coin six times, what is the probability of getting all heads?

Short Answer

Expert verified
The probability of getting all heads when tossing a fair coin six times is 0.015625.

Step by step solution

01

Understand the Problem

First, it is important to know that the coin is fair, which means the likelihood of landing heads (H) or tails (T) is the same. Second, the coin is tossed six times, and we are asked to find the probability of getting all heads (HHHHHH).
02

Determine the Probability of a Single Event

For a fair coin, the probability of landing heads (H) is 0.5. Since each event is independent, the probability of multiple events happening is simply the product of the probability of each event.
03

Calculate the Probability of All Events

Since there are 6 events (coin flips), and each has a 0.5 probability of happening, we simply need to calculate \(0.5^6 = 0.015625\). This is the likelihood of all six coin flips landing heads.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Enough curiosities involving the Fibonacci sequence exist to warrant a flourishing Fibonacci Association, which publishes a quarterly journal. Do some research on the Fibonacci sequence by consulting the Internet or the research department of your library, and find one property that interests you. After doing this research, get together with your group to share these intriguing properties.

Graph each of the functions in the same viewing rectangle. Describe how the graphs illustrate the Binomial Theorem. $$ \begin{array}{l}f_{1}(x)=(x+2)^{3} \\\f_{2}(x)=x^{3} \\\f_{3}(x)=x^{3}+6 x^{2} \\\f_{4}(x)=x^{3}+6 x^{2}+12 x \\\f_{5}(x)=x^{3}+6 x^{2}+12 x+8\end{array} $$ Use a \([-10,10,1]\) by \([-30,30,10]\) viewing rectangle.

Find the term indicated in each expansion. \((x-1)^{10} ;\) fifth term

Use the Binomial Theorem to find a polynomial expansion for each function. Then use a graphing utility and an approach similar to the one in Exercises 64 and 65 to verify the expansion. $$ f_{1}(x)=(x-1)^{3} $$

Find the term indicated in each expansion. \(\left(x^{3}+y^{2}\right)^{8} ;\) sixth term
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.