Question

One um contains two black balls (labeled B₁​ and B₂​ ) and a white ball (labeled W). A second um contains two white balls (labeled W₁ and W₂ ) and a black ball (labeled B). An experiment is performed in which one of the two ums is chosen at random and then two balls are randomly chosen from it one after another without replacement. i) Construct the possibility tree showing all possible outcomes of this experiment. ii) What is the total number of outcome of the experiment?

Answer 1

To construct the possibility tree, we need to first identify the two possible ums and the balls within each um. The possibility tree will have two branches: U1 and U2. Each branch will represent the um that is chosen at random. Under each branch, we will list the balls that can be chosen from that um. Then, we will list the balls that can be chosen from the remaining um under the other branch. This will give us a total of 6 possible outcomes.

Step-by-step explanation:

To construct the possibility tree, we need to first identify the two possible ums and the balls within each um. Let's label the first um as U1 and the second um as U2.

The balls in U1 are B1, B2, and W, and the balls in U2 are W1, W2, and B.

The possibility tree will have two branches: U1 and U2. Each branch will represent the um that is chosen at random. Under each branch, we will list the balls that can be chosen from that um.

Then, we will list the balls that can be chosen from the remaining um under the other branch. This will give us a total of 6 possible outcomes.

The total number of outcomes of the experiment is 6.