Ch. 4 - Probability

Triola - Elementary Statistics 14th Edition

Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook

Triola 14th Edition

Ch. 4 - Probability

Problem 4.1.27b

Chapter 4, Problem 4.1.27b

In Exercises 21-28, find the probability and answer the questions.

Genetics: Eye Color Each of two parents has the genotype brown/blue, which consists of the pair of alleles that determine eye color, and each parent contributes one of those alleles to a child. Assume that if the child has at least one brown allele, that color will dominate and the eyes will be brown. (The actual determination of eye color is more complicated than that.)

b. What is the probability that a child of these parents will have the blue/blue genotype?

Verified step by step guidance

Step 1: Understand the problem. Each parent has a genotype of brown/blue, meaning they can contribute either a 'brown' allele or a 'blue' allele to their child. The child’s genotype is determined by the combination of one allele from each parent. The possible genotypes are: brown/brown, brown/blue, and blue/blue. We are tasked with finding the probability that the child will have the blue/blue genotype.

Step 2: Determine the probability of each parent contributing a specific allele. Since each parent has one brown allele and one blue allele, the probability of contributing either allele is 50% or 0.5.

Step 3: Use the multiplication rule of probability. To have a blue/blue genotype, the child must receive a blue allele from both parents. The probability of this happening is the product of the probabilities of each parent contributing a blue allele: P(blue/blue) = P(parent 1 contributes blue) × P(parent 2 contributes blue).

Step 4: Substitute the probabilities into the formula. Since the probability of each parent contributing a blue allele is 0.5, the formula becomes P(blue/blue) = 0.5 × 0.5.

Step 5: Simplify the expression to find the probability. The result will give the probability that the child has the blue/blue genotype. Note that this is a straightforward application of basic probability rules.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Genotype and Alleles

A genotype refers to the genetic makeup of an organism, specifically the alleles it possesses for a particular trait. In this case, the parents have a genotype of brown/blue, meaning they carry one allele for brown eyes and one for blue. Alleles are different forms of a gene, and the combination of alleles inherited from each parent determines the child's genotype.

Dominance in Genetics

In genetics, dominance refers to the relationship between alleles, where one allele can mask the expression of another. The brown allele is dominant over the blue allele, meaning that if a child inherits at least one brown allele, the child's phenotype will be brown eyes. Understanding dominance is crucial for predicting the likelihood of certain traits appearing in offspring.

Punnett Square

A Punnett square is a diagram used to predict the genetic outcomes of a cross between two organisms. It helps visualize the possible combinations of alleles from the parents. In this scenario, constructing a Punnett square for the brown/blue genotypes of the parents will allow us to calculate the probability of the child having the blue/blue genotype, which is essential for answering the question.

Recommended video:

Guided course

04:48

Variance & Standard Deviation of Discrete Random Variables

Related Practice

Textbook Question

Alarm Clock Life Hack Each of us must sometimes wake up early for something really important, such as a final exam, job interview, or an early flight. (Professional golfer Jim Furyk was disqualified from a tournament when his cellphone lost power and he overslept.) Assume that a battery-powered alarm clock has a 0.005 probability of failure, a smartphone alarm clock has a 0.052 probability of failure, and an electric alarm clock has a 0.001 probability of failure.

b. If you use a battery-powered alarm clock and a smartphone alarm clock, what is the probability that they both fail? What is the probability that both of them do not fail?

Textbook Question

Births in Vietnam In Vietnam, the probability of a baby being a boy is 0.526 (based on the data available at this writing). For a family having four children, find the following.

b. The probability that all four children are girls.

Textbook Question

In Exercises 21-28, find the probability and answer the questions.

Guessing Birthdays On their first date, Kelly asks Mike to guess the date of her birth, not including the year.

b. Would it be unlikely for him to guess correctly on his first try?

views

Textbook Question

In Exercises 29 and 30, find the probabilities and indicate when the “5% guideline for cumbersome calculations” is used.

Medical Helicopters In a study of helicopter usage and patient survival, results were obtained from 47,637 patients transported by helicopter and 111,874 patients transported by ground (based on data from “Association Between Helicopter vs Ground Emergency Medical Services and Survival for Adults with Major Trauma,” by Galvagno et al., Journal of the American Medical Association, Vol. 307, No. 15).

b. If 5 of the subjects in the study are randomly selected without replacement, what is the probability that all of them were transported by helicopter?

Textbook Question

Births in the United States In the United States, the true probability of a baby being a boy is 0.512 (based on the data available at this writing). For a family having three children, find the following.

b. The probability that all three children are boys.

Textbook Question

In Exercises 21–24, use these results from the “1-Panel-THC” test for marijuana use, which is provided by the company Drug Test Success: Among 143 subjects with positive test results, there are 24 false positive (incorrect) results; among 157 negative results, there are 3 false negative (incorrect) results. (Hint: Construct a table similar to Table 4-1.)

Testing for Marijuana Use

b. How many of the subjects had a true negative result?