Question

A box contains 1 red and 3 identical white balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.

a) {(Red, White), (White, Red), (White, White)}
b) {(Red, Red), (White, White), (White, Red)}
c) {(Red, White), (Red, Red), (White, White)}
d) {(White, White), (White, Red), (Red, White)}

Answer 1

The correct sample space for the given experiment of drawing two balls without replacement from a box with 1 red and 3 white balls is a) {(Red, White), (White, Red), (White, White)}, representing all possible outcomes of the draws.

Step-by-step explanation:

The question requires us to determine the sample space of an experiment where two balls are drawn successively and without replacement from a box containing 1 red and 3 identical white balls. When drawing balls without replacement from a box, the available choices change after the first draw since the first ball is not returned to the box. Let us denote the balls as R for red and W for white.

The event of drawing a red ball first and a white ball second is denoted as (R, W). Similarly, the event of drawing a white ball first and a red ball second is denoted as (W, R), and drawing two white balls in succession is denoted as (W, W).

Considering all possible outcomes:

• The first ball drawn could be red, and since there's only one red ball, the second must be white, so we have (R, W).
• If the first ball is white, we could either draw a red ball second (W, R) or another white ball (W, W).

Hence, the complete sample space for this experiment is {(R, W), (W, R), (W, W)}. This means the correct answer to the question is:

a) {(Red, White), (White, Red), (White, White)}