Question

The numbers 1, 2, 3, and 4 are written separately on four slips of paper. The slips are put in a box and mixed thoroughly. A person draws two slips from the box, one after the other, without replacement. Describe the sample space for the experiment.

(a) {(1, 2), (1, 3), (1, 4), (2, 1), ...}
(b) {(1, 2), (2, 1), (1, 3), (3, 1), ...}
(c) {(1, 1), (1, 2), (1, 3), (1, 4), ...}
(d) {(1, 2), (2, 3), (3, 4), (4, 1), ...}

Answer 1

The correct sample space for drawing two slips without replacement is option (a) {(1, 2), (1, 3), (1, 4), (2, 1), ...}, displaying all possible ordered pairs of numbers.

Step-by-step explanation:

The correct sample space for the experiment of drawing two slips of paper from a box containing the numbers 1, 2, 3, and 4, without replacement, is: option (a) {(1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (2, 4), (3, 1), (3, 2), (3, 4), (4, 1), (4, 2), (4, 3)}. This sample space lists all possible ordered pairs of numbers that can be drawn, ensuring that once a number is drawn, it is not replaced, thus it does not appear again in the pair.

The first number in each pair represents the first slip drawn, and the second number represents the second slip drawn. It is important to include both (1, 2) and (2, 1) since the order matters and these represent different outcomes. Since there are four slips and two are drawn, the total number of possible outcomes is 4*(4-1) = 12. Each outcome is equally likely if the slips are well-shuffled and drawn randomly, so each has a probability of 1/12. This foundational concept of sample space is important for calculating probabilities of various outcomes in probability theory.