Question

question 8 of 10
a coin has 2 sides: heads (h) and tails (t). a bag has 4 balls: 1 red (r), 1 green (g), 1 yellow (y), and 1 orange (o).
you toss a coin and randomly pick a ball. what is the sample space?
a. {r, g, y, o, h, t}
b. {hr, hg, hy, ho, tr, tg, ty, to}
c. {tr, tg, hy, ho}
d. {h, t}

Explanation:

Step1: Understand the sample - space concept

The sample space is the set of all possible outcomes.

Step2: Analyze the two - step experiment

When tossing a coin, there are 2 outcomes (H or T). When picking a ball, there are 4 outcomes (R, G, Y, O).

Step3: Use the counting principle for combined outcomes

For each coin outcome (H or T), it can combine with each ball outcome.

• If the coin shows H, the combined outcomes are HR, HG, HY, HO.
• If the coin shows T, the combined outcomes are TR, TG, TY, TO.

So the sample space is {HR, HG, HY, HO, TR, TG, TY, TO}.

Answer:

B. {HR, HG, HY, HO, TR, TG, TY, TO}