menu
bartleby
search
close search
Hit Return to see all results

Red snapper is a rare and expensive reef fish served at upscale restaurants. Federal law prohibits restaurants from serving a cheaper look-alike variety of fish (e.g. vermillion snapper or lane snapper) to customers who order red snapper. Researchers at the University of North Carolina used DNA analysis to examine fish specimens labeled “red snapper” that were purchased from vendors across the country. The DNA tests revealed that 77% of the specimens were not red snapper but the cheaper look-alike variety of fish.a.Assuming the results of the DNA analysis are valid, what is the probability that you are actually served red snapper the next time you order it at a restaurant?b.If there are five customers at a restaurant, all who have ordered red snapper, what is the probability that at least one customer is actually served red snapper?

Question
Red snapper is a rare and expensive reef fish served at upscale restaurants. Federal law prohibits restaurants from serving a cheaper look-alike variety of fish (e.g. vermillion snapper or lane snapper) to customers who order red snapper. Researchers at the University of North Carolina used DNA analysis to examine fish specimens labeled “red snapper” that were purchased from vendors across the country. The DNA tests revealed that 77% of the specimens were not red snapper but the cheaper look-alike variety of fish.
a.
Assuming the results of the DNA analysis are valid, what is the probability that you are actually served red snapper the next time you order it at a restaurant?
b.
If there are five customers at a restaurant, all who have ordered red snapper, what is the probability that at least one customer is actually served red snapper?
check_circleAnswer
Step 1

There are only two possible outcomes when you order red snapper - you either get red snapper or the cheaper look-alike. 

Let A be the event that red-snapper is served.

Let B be the event that the cheaper look-alike is served.

Both the outcomes are mutually exclusive ie they can't occur simultaneously.  ie P(AnB)= 0

DNA analysis says that 77% of the fish specimens labelled red snapper were not actually red snapper but the cheaper look-alike. So the probability of getting the cheaper look-alike of red snapper on ordering red snapper is 0.77.

This can be written as, P(B) = 0.77

a)

As there are only two mutually exclusive outcomes, we know that   P(A) + P(B) = 1

P(A) = 1 - P(B)  = 1 - 0.77 = 0.23

Therefore, probability of getting red snapper is 0.23

Step 2

b)

There can be  6 possible outcomes when 5 customers order red snapper.

P(0) = no customer gets red snapper 

P(1)= exactly 1 customer gets red snapper 

P(2)= exactly 2 customers get red snapper

P(3)= exactly 3 customers get red snapper

P(4)= exactly 4 customers get red snapper

P(5)= All 5 customers get red snapper 

As there are just 6 outcomes, P(0) + P(1) + P(2) + P(3) + P(4) + P(5) = 1                .......................equation 1

When there are 5 people i...

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Our solutions are written by experts, many with advanced degrees, and available 24/7

See Solution
Tagged in

Math

Statistics

Other

Related Statistics Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: A test consists of 940 true or false questions. If the student guesses on each​ question, what is th...

A: Given number of true or false questions = n = 940.Probability of correct answer p = 1/2Here we can s...

question_answer

Q: Flying over the western states with mountainous terrain in a small aircraft is 40% riskier than flyi...

A: (a) Poisson distribution is a good choice for the probability distribution of r:Poisson distribution...

question_answer

Q: Do most researchers still insist on at least interval level of measurement as a condition for the us...

A: Solution:In Interval scale, the difference between two values are standardized and equal. Most stati...

question_answer

Q: A grocery store manager did a study to look at the relationship between the amount of time (in minut...

A: The estimated regression line is as follows:

question_answer

Q: How to determine Estimate the P-value.

A: Introduction:P-value: The P-value is the probability of obtaining a test statistic value as extreme ...

question_answer

Q: Please answer the whole question  (2) Let x be the age of a licensed driver in years. Let y be the p...

A: (a) Scatter diagram of the data:The scatter diagram for the given data that is obtained using EXCEL ...

question_answer

Q: Intelligence quotas on two different tests are normally distributed. Test A has a mean of 100 and a ...

A: In this question, it has been given that two different tests A and B are normally distributed, Test ...

question_answer

Q: What is the condition on the probability of success p that will guarantee the histogram of a binomia...

A: The binomial distribution has p - probability of success and n- number of trails. The binomial distr...

question_answer

Q: Let x be per capita income in thousands of dollars. Let y be the number of medical doctors per 10,00...

A: Hi, since the problem posted by you contains multiple sub-parts, we are answering the first three su...

Sorry about that. What wasn’t helpful?