Question

a deck of cards contains 8 cards. there are 4 red and 4 blue cards. each of the colored cards is numbered 1 through 4. let x be the event that two randomly drawn cards have a sum that is an even number. which event is a subset of event x? the product of the cards is even. both cards are the same number. both cards are the same color. at least one card is red.

Explanation:

Step1: Recall sum - parity rules

The sum of two numbers is even if both numbers are even or both numbers are odd.

Step2: Analyze each option

• Option 1: The product of the cards is even. This doesn't guarantee the sum is even. For example, 2 and 3 have an even product but an odd sum.
• Option 2: If both cards are the same number, say \(n\), then the sum is \(n + n=2n\) which is even. So, if this event occurs, the sum of the two - card draw is even. This event is a subset of event \(X\).
• Option 3: Both cards being the same color doesn't guarantee the sum is even. For example, two red cards with numbers 1 and 2 have an odd sum.
• Option 4: At least one card is red doesn't guarantee the sum is even. For example, a red 1 and a blue 2 have an odd sum.

Answer:

Both cards are the same number.