In the city of Savannah, Georgia, 22% of young couples take wedding pictures along the Riverwalk (R), and 42% of young couples take wedding pictures in one of the many historical squares (S) throughout the city. However, only 14% of young couples take wedding pictures along the Riverwalk and in the squares. Are these two events independent of each other? Include the reason why or why not.       A. The events aren't independent, because P(R) × P(S) ≠ P(P and S).  B. The events are independent, because P(R) × P(S) ≠ P(P and S).  C. The events aren't independent, because P(R) × P(S) = P(P and S).  D. The events are independent, because P(R) × P(S) = P(P and S)

Question
Asked Mar 22, 2019
In the city of Savannah, Georgia, 22% of young couples take wedding pictures along the Riverwalk (R), and 42% of young couples take wedding pictures in one of the many historical squares (S) throughout the city. However, only 14% of young couples take wedding pictures along the Riverwalk and in the squares. Are these two events independent of each other? Include the reason why or why not. 
    
  A. The events aren't independent, because P(R) × P(S) ≠ P(P and S).
  B. The events are independent, because P(R) × P(S) ≠ P(P and S).
  C. The events aren't independent, because P(R) × P(S) = P(P and S).
  D. The events are independent, because P(R) × P(S) = P(P and S)
check_circleExpert Solution
Step 1

Given information:

Denote the event of young couples take wedding pictures along with the river walk as R,

It is given that, 22% of young couples take wedding pictures along with the river walk.

That is, the probability that the young couples take wedding pictures along with the river walk is P(R) = 0.22.

Denote the event of young couples take wedding pictures in one of the many historical squares as S,

It is given that, 42% of young couples take wedding pictures in one of the many historical squares.

That is, the probability that the young couples take wedding pictures in one of the many historical squares is P(S) = 0.42.

Furthermore, it is given that, 14% of young couples take wedding pictures along with the river walk and in one of the many historical squares.

That is, the probability that the young couples take wedding pictures along with the river walk and in one of the many historical squares is P(R and S) = 0.14.

Step 2

Independent events:

Two or more events are said to be independent if occurrence of one does not affect the occurrence of other. In other words, it can be said that, independent events do not affect the probability of occurrence of one another. That is, independent events can happen at the same time.

Let R and S are two independent events, then the probability of occurrence of the event R will not affect the probability of occurrence of the event S.

Example:

Getting a head in the first toss of a coin and getting a tail in the second toss of a coin.

The union, intersection and conditional probabilities of independent events are given below:

fullscreen
Step 3

Check whether or not the two events R and S are independent:

For the events R and S to be independent, P(R and S) must be equal to the product of P(R) and P(S). That is, P(R and S) = P(R) * P(S).

The probability value obtained below does not satisfy the requirement of the independent events.

Therefore, the events R and S a...

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour*

See Solution
*Response times may vary by subject and question
Tagged in

Math

Statistics

Related Statistics Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: Workers at a large toxic cleanup project are concerned that their white blood cell counts may have b...

A: Let the random variable X be the white blood cell count per cubic millimetre of whole blood in a hea...

question_answer

Q: Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as ...

A: Hello there! there are moe than three subparts in the question. According to our policies cannot ans...

question_answer

Q: Consider a drug testing company that provides a test for marijuana usage. Among 301 tested subjects,...

A: Given hypothesis testp be the proportion of wrong test results Null hypothesis : p = 0.10Alternate H...

question_answer

Q: The Toylot company makes an electric train with a motor that it claims will draw an average of only ...

A: The provided information are:

question_answer

Q: A marketing manager for a cell phone company claims that more than 55% of children aged 8-12 have ce...

A: Null and alternative hypotheses:Here, to check whether more than 55% of children aged 8-12 have cell...

question_answer

Q: Construct a probability distribution for the data and draw a graph for the distribution.  Find the m...

A: The probability distribution is given by:

question_answer

Q: A medical researcher wants to construct a 95% confidence interval for the proportion of knee replace...

A: Sample size:The minimum sample size for a desired confidence level, α with a given margin of error, ...

question_answer

Q: Consider the following multiple regression model :          y hat = -6.72 + 0.51x1 - 0.69x2 + 1.452x...

A: The given multiple regression model is as follows:

question_answer

Q: Linear Programming Problem A manufacturer of three models of tote bag must determine the production ...

A: This can be solved using Solver tool in Excel. Go to Data tab in Excel and check if you see Solver u...