A bag two blue balls and three pink balls. A ball is selected from the bag at random but not replaced. A second ball is then drawn, and again, not replaced. Use a tree diagram to determine the sample space. (3 marks)
Question
A bag two blue balls and three pink balls. A ball is selected from the bag at random but not replaced. A second ball is then drawn, and again, not replaced. Use a tree diagram to determine the sample space. (3 marks)
Solution
Step 1: Draw the first branch of the tree diagram. This represents the first ball drawn. There are two possibilities: a blue ball (B1) or a pink ball (P1).
Step 2: From each of these possibilities, draw two more branches. These represent the second ball drawn. If the first ball was blue, the second ball could be one of the remaining blue ball (B2) or one of the three pink balls (P2). If the first ball was pink, the second ball could be one of the two blue balls (B2) or one of the remaining two pink balls (P2).
Step 3: Label each end of the branches with the outcome. This gives us the sample space.
The sample space is: {B1B2, B1P2, P1B2, P1P2}.
This means the possible outcomes are: drawing two blue balls, drawing a blue ball then a pink ball, drawing a pink ball then a blue ball, or drawing two pink balls.
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