Answer-first summary for fast verification
Answer: 2/3
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: 1. **Bag 1:** 3 square + 2 round = 5 total blocks 2. **Bag 2:** 2 square + 3 round = 5 total blocks 3. **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.
Author: Nikitesh Somanthe
Ultimate access to all questions.
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?
A
1/5
B
1/3
C
2/5
D
2/3
No comments yet.