  # 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
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:

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...

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