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?
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Community
NNikitesh
A
1/5
B
1/3
C
2/5
D
2/3
Explanation:
The correct answer is D) 2/3.
Explanation:
This is a probability problem using the law of total probability. We have three bags, each with different compositions of square and round blocks:
- Bag 1: 3 square + 2 round = 5 total blocks
- Bag 2: 2 square + 3 round = 5 total blocks
- Bag 3: 0 square + 5 round = 5 total blocks
Since a bag is randomly chosen first, each bag has probability P(bag) = 1/3.
Now we calculate the probability of drawing a round block from each bag:
- P(Round | Bag 1) = 2/5
- P(Round | Bag 2) = 3/5
- P(Round | Bag 3) = 5/5 = 1
Using the law of total probability: P(Round) = P(Round|Bag 1) × P(Bag 1) + P(Round|Bag 2) × P(Bag 2) + P(Round|Bag 3) × P(Bag 3)
P(Round) = (2/5) × (1/3) + (3/5) × (1/3) + (1) × (1/3) P(Round) = 2/15 + 3/15 + 5/15 P(Round) = 10/15 = 2/3
Therefore, the probability of choosing a round block is 2/3.
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