/*! 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 8 Find the probability. In China... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 8

Find the probability. In China, where many couples were allowed to have only one child, the probability of a baby being a boy was \(0.545 .\) Among six randomly selected births in China, what is the probability that at least one of them is a girl? Could this system continue to work indefinitely? (Phasing out of this policy was begun in 2015.)

Short Answer

Expert verified
The probability that at least one of six births is a girl is 0.944. Considering social and demographic impacts, the policy could not work indefinitely.

Step by step solution

01

Determine the Probability of a Girl

Given the probability of a baby being a boy is 0.545, the probability of a baby being a girl is calculated as: P(Girl) = 1 - P(Boy) = 1 - 0.545 = 0.455
02

Calculate the Probability of All Boys

To find the probability that all six births are boys, use the formula for the probability of independent events: P(All Boys) = (P(Boy))^6 = (0.545)^6
03

Use the Complement Rule

The probability of at least one girl is the complement of the probability that all six are boys: P(At least one girl) = 1 - P(All Boys)
04

Perform the Calculations

First, calculate (0.545)^6 Then, calculate 1 - (0.545)^6 Using a calculator: P(All Boys) 鈮� 0.056 Therefore, P(At least one girl) = 1 - 0.056 = 0.944
05

Discuss Feasibility of the Policy

While the probability of at least one girl in six births is high, other social and demographic factors must be considered. Policies like the one-child policy can lead to skewed sex ratios and other long-term demographic issues, making it challenging to sustain indefinitely.

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.

probability calculation
Probability calculation is fundamental in understanding how likely an event is to happen. In this exercise, we calculated the probability that at least one of six births in China is a girl, given the probability of a boy being 0.545.
Let's break it down:
  • First, we needed to find the probability of a baby being a girl, which was calculated by subtracting the probability of a boy from 1.
  • Next, we used this probability to determine the likelihood of all six births being boys.
  • Finally, we used the complement rule to find the probability of at least one girl.
This way of step-by-step calculation helps us systematically solve probability problems.
independent events
Understanding independent events is crucial in probability theory. Independent events are those whose outcomes do not affect each other. In our exercise, each birth being a boy or a girl is an independent event because the outcome of one birth does not influence the others.
To calculate the probability of all six births being boys, we multiplied the probability of a boy in a single birth by itself six times:
\[(P(Boy))^6\]
This formula shows that the probability of multiple independent events occurring together can be found by multiplying their individual probabilities.
complement rule
The complement rule is used to find the probability that an event does not happen by subtracting the event's probability from 1. It helps deal with 'at least one' type of probability problems, like our exercise.
In our exercise, we calculated the probability of all six births being boys and then used the complement rule to find the probability of at least one girl:
\[P(\text{At least one girl}) = 1 - P(\text{All Boys})\]
This simplifies the calculation, especially when direct calculation might be complex or cumbersome.
demographic policy impact
Demographic policies, like China's one-child policy, can have significant long-term effects. These policies influence population structure and social dynamics.
Despite the high probability (0.944) of at least one girl in six births, policies that limit family size can result in skewed gender ratios and aging populations.
Over time, these effects can lead to challenges like labor shortages and increased pressure on social services. It is essential to consider these demographic impacts when evaluating the feasibility of such policies.

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

Find the probability. Subjects for the next presidential election poll are contacted using telephone numbers in which the last four digits are randomly selected (with replacement). Find the probability that for one such phone number, the last four digits include at least one \(0 .\)

Express the indicated degree of likelihood as a probability value between 0 and \(1 .\) Benjamin Franklin said that death is a certainty of life.

A study addressed the issue of whether pregnant women can correctly predict the gender of their baby. Among 104 pregnant women, 57 correctly predicted the gender of their baby (based on data from "Are Women Carrying 'Basketballs'...," by Perry, DiPietro, Constigan, Birth, Vol. 26, No. 3). If pregnant women have no such ability, there is a \(0.327\) probability of getting such sample results by chance. What do you conclude?

"Who discovered penicillin: Sean Penn, William Penn. Penn Jillette, Alexander Fleming, or Louis Pasteur?" If you make a random guess for the answer to that question, what is the probability that your answer is the correct answer of Alexander Fleming?

Nasonex is a nasal spray used to treat allergies. In clinical trials, 1671 subjects were given a placebo, and 2 of them developed upper respiratory tract infections. Another 2103 patients were treated with Nasonex and 6 of them developed upper respiratory tract infections. Assume that Nasonex has no effect on upper respiratory tract infections so that the rate of those infections also applies to Nasonex users. Using the placebo rate of \(2 / 1671\), simulate groups of 2103 subjects given the Nasonex treatment, and determine whether a result of 6 upper respiratory tract infections could easily occur. What does that suggest about Nasonex as a cause of upper respiratory tract infections?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Geometry

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.