/*! 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 37 Assume equally likely outcomes. ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 14: Problem 37

Assume equally likely outcomes. Determine the probability of having 3 boys in a 3 -child family.

Short Answer

Expert verified
The probability is \( \frac{1}{8} \).

Step by step solution

01

Determine Total Possible Outcomes

First, calculate the total number of possible outcomes for a 3-child family. Each child can be either a boy (B) or a girl (G). Therefore, the total number of possible outcomes is given by the combinations of B and G over 3 children. This results in: \[ 2^3 = 8 \] The possible outcomes are: BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG.
02

Determine Favorable Outcomes

Next, identify the outcomes where there are exactly 3 boys. The only combination that meets this criteria is BBB. Hence, there is 1 favorable outcome.
03

Calculate Probability

Finally, calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes: \[ P(\text{3 boys}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{8} \]

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Equally Likely Outcomes
In probability, equally likely outcomes mean that each possible result of an event has the same chance of occurring. Imagine flipping a fair coin: it has two equally likely outcomes, heads or tails.
When we talk about equally likely outcomes for a 3-child family, each child has an equal chance of being a boy (B) or a girl (G).
This assumption of equally likely outcomes simplifies our calculations, as every scenario (like BBB or GGG) has the same chance of happening.
Combinations
Combinations help us understand how different groups can form. For example, in a family with 3 children, each can either be a boy (B) or a girl (G).
This gives us several possible combinations of genders.
We calculate it as \(2^3 = 8\), showing all possible groupings (like BBB, BBG, etc.).
The idea of combinations is crucial in figuring out total possible outcomes and finding specific groups among those combinations.
Favorable Outcomes
Favorable outcomes refer to the specific results that meet our criteria for an event. For instance, if we want exactly 3 boys in a 3-child family, BBB is our favorable outcome.
Out of all the possible combinations (BBB, BBG, etc.), we only consider outcomes that fit what we're looking for.
In this case, we count only 1 favorable outcome (BBB).
Total Possible Outcomes
Total possible outcomes count all the different results that could occur from an event. For a 3-child family, each child can be a boy or girl.
Hence, with two choices per child over 3 children, we calculate \[2^3 = 8\ \] different outcomes, like BBB, BGB, etc.
Listing all these outcomes helps us understand the full range of possibilities, making it easier to see the chance of a specific favorable outcome occurring.

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

List the sample space S of each experiment and (b) construct a probability model for the experiment. Tossing one fair coin three times

Explain the difference between a permutation and a combination. Give an example to illustrate your explanation.

Human blood is classified as either \(\mathrm{Rh}+\) or \(\mathrm{Rh}-.\) Blood is also classified by type: \(\mathrm{A},\) if it contains an A antigen but not a \(B\) antigen; \(B\), if it contains a \(\mathrm{B}\) antigen but not an \(\mathrm{A}\) antigen; \(\mathrm{AB},\) if it contains both \(\mathrm{A}\) and \(B\) antigens; and \(O\), if it contains neither antigen. Draw a Venn diagram illustrating the various blood types Based on this classification, how many different kinds of blood are there?

How many two-letter codes can be formed using the letters \(A, B, C,\) and \(D ?\) Repeated letters are allowed.

List all the permutations of 6 objects \(1,2,3,4,5,\) and 6 choosing 3 at a time without repetition. What is \(P(6,3) ?\)
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Calculus

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.