A coin has 2 sides: heads (H) and tails (T). A bag has 4 balls: 1 blue (B), 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.{TB, TG, HY, HO}C.{HB, HG, HY, HO, TB, TG, TY, TO}D.{B, G, Y, O, H, T}
Question
A coin has 2 sides: heads (H) and tails (T). A bag has 4 balls: 1 blue (B), 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.{TB, TG, HY, HO}C.{HB, HG, HY, HO, TB, TG, TY, TO}D.{B, G, Y, O, H, T}
Solution
The sample space is all possible outcomes of a random experiment. In this case, the experiment involves two steps: tossing a coin and picking a ball.
The coin has two possible outcomes: heads (H) and tails (T).
The bag has four possible outcomes: blue (B), green (G), yellow (Y), and orange (O).
Therefore, each toss of the coin can be paired with each pick from the bag, resulting in 2 * 4 = 8 possible outcomes.
These outcomes are: heads and blue (HB), heads and green (HG), heads and yellow (HY), heads and orange (HO), tails and blue (TB), tails and green (TG), tails and yellow (TY), and tails and orange (TO).
So, the sample space is {HB, HG, HY, HO, TB, TG, TY, TO}, which corresponds to option C.
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