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.{H, T}B.{HR, HG, HY, HO, TR, TG, TY, TO}C.{TR, TG, HY, HO}D.{R, G, Y, O, H, T}
Question
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.{H, T}B.{HR, HG, HY, HO, TR, TG, TY, TO}C.{TR, TG, HY, HO}D.{R, G, Y, O, H, T}
Solution
The sample space of an experiment is the set of all possible outcomes. In this case, the experiment involves two steps: tossing a coin and picking a ball.
Step 1: Tossing a coin The coin has two sides: heads (H) and tails (T). So, the possible outcomes for this step are {H, T}.
Step 2: Picking a ball The bag has 4 balls: red (R), green (G), yellow (Y), and orange (O). So, the possible outcomes for this step are {R, G, Y, O}.
Because these two steps are performed together, we need to consider all possible combinations of outcomes. This gives us the following sample space:
{HR, HG, HY, HO, TR, TG, TY, TO}
So, the correct answer is B.{HR, HG, HY, HO, TR, TG, TY, TO}.
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