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At Least One. In Exercises 5鈥12, find the probability.

Three Girls Find the probability that when a couple has three children, at least one of them is a girl. (Assume that boys and girls are equally likely.)

Short Answer

Expert verified

The probability of having at least one girl out of three children is equal to 0.875.

Step by step solution

01

Given information

A couple has three children.

The chances of having a girl or a boy are even.

02

Define the concept of probability for the event of “At least One”

In the event of selecting elements from a sample space,the probability of getting 鈥渁t least one鈥 of a specific type of item is the probability of gettingone or more than one of that item.

The probability of selecting at least one of a unit is the complementary event of selecting none of those.

It also follows the property:

Patleastone=1-Pnone

03

Identify the sample space of three children

The sample space for the gender of the three children is as follows:

S = {bbb,bbg,bgb,gbb,bgg,gbg,ggb,ggg}

Here, b represents the male gender, whereas g represents the female gender.

The probability of having at least one girl denotes the probability of having one or more than one girl.

It can also be written as one minus the probability of having no girl.

The number of favorable outcomes of having no girl = 1.

The total number of outcomes = 8.

Patleast1girl=1-Pnogirl=1-18=78=0.875

Therefore, the probability of having at least one girl is equal to 0.875.

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Most popular questions from this chapter

At Least One. In Exercises 5鈥12, find the probability.

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Probability from a Sample Space. In Exercises 33鈥36, use the given sample space or construct the required sample space to find the indicated probability.

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Developed Flu

Did not develop Flu

Vaccine Treatment

14

1056

Placebo

95

437

If 1 of the 1602 subjects is randomly selected, find the probability of getting 1 that developed flu.

In Exercises 9鈥20, use the data in the following table, which lists drive-thru order accuracy at popular fast food chains (data from a QSR Drive-Thru Study). Assume that orders are randomly selected from those included in the table.

惭肠顿辞苍补濒诲鈥檚

Burger King

奥别苍诲测鈥檚

Taco Bell

Order Accurate

329

264

249

145

OrderNotAccurate

33

54

31

13

Fast Food Drive-Thru Accuracy If two orders are selected, find the probability that they are both accurate.

a. Assume that the selections are made with replacement. Are the events independent?

b. Assume that the selections are made without replacement. Are the events independent?

In Exercises 25鈥32, find the probability and answer the questions.

X-Linked Genetic Disease Men have XY (or YX) chromosomes and women have XX chromosomes. X-linked recessive genetic diseases (such as juvenile retinoschisis) occur when there is a defective X chromosome that occurs without a paired X chromosome that is not defective. In the following, represent a defective X chromosome with lowercase x, so a child with the xY or Yx pair of chromosomes will have the disease and a child with XX or XY or YX or xX or Xx will not have the disease. Each parent contributes one of the chromosomes to the child.

a. If a father has the defective x chromosome and the mother has good XX chromosomes, what is the probability that a son will inherit the disease?

b. If a father has the defective x chromosome and the mother has good XX chromosomes, what is the probability that a daughter will inherit the disease? c. If a mother has one defective x chromosome and one good X chromosome and the father has good XY chromosomes, what is the probability that a son will inherit the disease?

d. If a mother has one defective x chromosome and one good X chromosome and the father has good XY chromosomes, what is the probability that a daughter will inherit the disease?

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