Question

slips of paper marked with the numbers 1, 2, 3, and 4 are placed in a box. after being mixed, two slips are drawn simultaneously. write out the sample space s, choosing an s with equally likely outcomes, if possible. then give the value of n(s) and tell whether the outcomes in s are equally likely. finally, write the indicated events below in set notation.
a. both slips are marked with even numbers.
b. one slip is marked with an odd number and the other is marked with an even number.
c. both slips are marked with the same number.

are the outcomes equally likely?
✓ yes
○ no

a. write the event both slips are marked with even numbers.
○ a. {(1,2), (1,3), (1,4), (2,3), (2,4), (3,4)}
○ b. {(2,4)}
○ c. {2, 4}
○ d. ∅

Explanation:

Step1: Identify even numbers

The even numbers from 1, 2, 3, 4 are 2 and 4.

Step2: Determine pairs of even numbers

We need to find the set of pairs where both numbers are even. The possible pairs when drawing two slips (order doesn't matter in simultaneous draw, but the pairs are unordered). The only pair with both even numbers is (2, 4). Also, since the draw is simultaneous, (4, 2) is the same as (2, 4), so the set of outcomes where both are even is {(2, 4)}. Now let's analyze the options:

• Option A: This set includes pairs with odd and even numbers, so it's not just even - even pairs.
• Option B: {(2, 4)} is the set of pairs where both numbers are even (2 and 4 are even).
• Option C: This is a set of numbers, not pairs of numbers (since we are drawing two slips, the outcomes should be pairs).
• Option D: The empty set is incorrect because there is a valid pair (2, 4) with both even numbers.

Answer:

B. {(2,4)}