Kids A couple plans to have children until they get a girl,...

Name: Problem 13, Chapter 14: Stats Data and Models
Uploaded: 2023-07-21T01:12:03-08:00
Duration: 3 min 34 s
Channel: Sheryl Ezze
Description: Kids A couple plans to have children until they get a girl, but they agree that they will not have more than three children even if all are boys. (Assume boys and girls are equally likely.) a. Create a probability model for the number of children they might have. b. Find the expected number of children. c. Find the expected number of boys they'll have.

Kids A couple plans to have children until they get a girl, but they agree that they will not have more than three children even if all are boys. (Assume boys and girls are equally likely.) a. Create a probability model for the number of children they might have. b. Find the expected number of children. c. Find the expected number of boys they'll have.

Kids A couple plans to have children until they get a girl, but they agree that they will not have more than three children even if all are boys. (Assume boys and girls are equally likely.)
a. Create a probability model for the number of children
they might have.
b. Find the expected number of children.
c. Find the expected number of boys they'll have.

Key Concepts

Truncated Distributions and Stopping Rules

Truncated distributions occur when the underlying random process is limited by an imposed boundary, such as a maximum number of trials or outcomes. Stopping rules are the criteria that determine when the experiment is halted, which in turn affects the distribution of outcomes. Understanding these concepts is important for accurately modeling real-world situations where experiments do not continue indefinitely.

Probability Model

A probability model provides a systematic way to describe a random experiment by listing all possible outcomes and assigning a probability to each. This concept is central to probability theory and underpins the formulation of problems by establishing the sample space and the methods for calculating the likelihood of various events.

Expected Value

The expected value is a fundamental concept in probability and statistics that represents the long-run average outcome of a random variable if an experiment were repeated many times. It involves summing the products of each outcome with its corresponding probability, and it is used to assess the central tendency or mean behavior of the probability distribution.

Transcript

00:01 So we have a couple plans to have children until they have a girl, but they agree that they will not have more than three children, even if they're all boys.

00:09 So what could happen? they could have a girl, they could have a boy, and then a girl.

00:14 They could have a boy, a boy, and a boy, and then stop.

00:20 Or they could have a boy, a boy, and then a girl, and stop.

00:24 And so we want to create, first of all, a model that will have the number of children, that will be born.

00:35 And so we can see that they can have, for part a, they can have one child, and that would be a 50 % chance of having a girl on the first child.

00:49 They could have two children, and that's going to be .5 times .5, which is going to be .25.

00:56 And then they could have three children.

00:58 And there are two ways for that to happen, and this is a 1 8th chance, plus a 1 8th chance, 1 half times 1 half times 1 half.

01:05 And that's 2 8ths, which again is .25.

01:09 And then we have to find what the expected number of children is.

01:14 So our expected number of children is to take this 1, 1 times .5, plus 2 times .25, it's supposed to be just a 2, plus 3 times .25.

01:40 And so that's going to be .5, .5 plus 2 times that is going to be .5, plus 3 times that is going to be .75.

01:56 And so that's going to add up to 1 .75 children.

02:01 That's the average how many they'll have.

02:03 Now on part c, we want to determine what is the expected number of boys they'll have...

Please give Ace some feedback