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.

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

Explanation:

Step1: Understand the Problem

We have slips with numbers 1, 2, 3, 4. We draw two slips simultaneously. We need to find the event where both slips have the same number.

Step2: Analyze Possible Outcomes

When drawing two slips, the possible pairs are combinations (since order doesn't matter in simultaneous drawing, but let's check the sample space). The sample space for drawing two slips from 1,2,3,4 is \( S=\{(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)\} \). Now, we need to find pairs where both numbers are the same. But we have only one slip of each number (1, 2, 3, 4). So, there are no pairs where both numbers are the same.

Step3: Determine the Event Set

The event "both slips are marked with the same number" has no elements because we can't draw two slips with the same number (since there's only one slip for each number). So the set is the empty set \( \varnothing \).

Answer:

D. \( \varnothing \)