Financial Risk Manager Part 1
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There are three different bags. The first bag contains 3 square blocks and 2 round blocks. The second bag contains 2 square blocks and 3 round blocks. The third bag contains 5 round blocks. In an experiment, a bag is randomly chosen, and then a block is chosen from the bag. What is the probability that a round block is chosen?
Explanation:
Explanation
This is a probability problem using the law of total probability. Let's define the events:
- P(R) = Probability that the block is round
- P(R|1) = Probability that the block is round given that it is from the first bag = 2/5
- P(R|2) = Probability that the block is round given that it is from the second bag = 3/5
- P(R|3) = Probability that the block is round given that it is from the third bag = 5/5 = 1
Since each bag is equally likely to be chosen:
- P(1) = P(2) = P(3) = 1/3
Using the law of total probability:
P(R) = P(R|1) × P(1) + P(R|2) × P(2) + P(R|3) × P(3)
P(R) = (2/5) × (1/3) + (3/5) × (1/3) + 1 × (1/3)
P(R) = (2/15) + (3/15) + (5/15) = 10/15 = 2/3
Therefore, the probability that a round block is chosen is 2/3.