Questions: Select the correct answer. Which statement is a converse of p ? p : If every fourth card drawn is a spade, then 25% of the cards in a deck would be spades. A. If 25% of the cards in a deck are spades, then every fourth card drawn would be a spade. B. If every fourth card drawn isn't a spade, then 25% of the cards in a deck aren't spades. C. If 25% of the cards in a deck aren't spades, then every fourth card drawn wouldn't be a spade. D. If every fourth card drawn isn't a spade, then 75% of the cards in a deck are spades.

Select the correct answer.

Which statement is a converse of p ?
p : If every fourth card drawn is a spade, then 25% of the cards in a deck would be spades.
A. If 25% of the cards in a deck are spades, then every fourth card drawn would be a spade.
B. If every fourth card drawn isn't a spade, then 25% of the cards in a deck aren't spades.
C. If 25% of the cards in a deck aren't spades, then every fourth card drawn wouldn't be a spade.
D. If every fourth card drawn isn't a spade, then 75% of the cards in a deck are spades.

Transcript text: Select the correct answer. Which statement is a converse of $p$ ? $p$ : If every fourth card drawn is a spade, then $25 \%$ of the cards in a deck would be spades. A. If $25 \%$ of the cards in a deck are spades, then every fourth card drawn would be a spade. B. If every fourth card drawn isn't a spade, then $25 \%$ of the cards in a deck aren't spades. C. If $25 \%$ of the cards in a deck aren't spades, then every fourth card drawn wouldn't be a spade. D. If every fourth card drawn isn't a spade, then $75 \%$ of the cards in a deck are spades.

Solution

Solution Steps

To find the converse of a statement, we need to switch the hypothesis and the conclusion. The original statement $p$ is "If every fourth card drawn is a spade, then $25 \%$ of the cards in a deck would be spades." The converse would be "If $25 \%$ of the cards in a deck are spades, then every fourth card drawn would be a spade." Therefore, the correct answer is option A.

Step 1: Identify the Original Statement

The original statement $ p $ is: "If every fourth card drawn is a spade, then $ 25\% $ of the cards in a deck would be spades."

Step 2: Formulate the Converse

To find the converse of the statement, we switch the hypothesis and conclusion. The converse is: "If $ 25\% $ of the cards in a deck are spades, then every fourth card drawn would be a spade."

Step 3: Analyze the Options

We compare the converse with the provided options:

A: "If $ 25\% $ of the cards in a deck are spades, then every fourth card drawn would be a spade." (This matches the converse.)
B: "If every fourth card drawn isn't a spade, then $ 25\% $ of the cards in a deck aren't spades."
C: "If $ 25\% $ of the cards in a deck aren't spades, then every fourth card drawn wouldn't be a spade."
D: "If every fourth card drawn isn't a spade, then $ 75\% $ of the cards in a deck are spades."

Step 4: Determine the Correct Answer

The correct option that represents the converse of the original statement is option A.