Answer: 3/10

## Explanation This is a **Bayes' Theorem** problem where we need to find the conditional probability that the block came from the second bag given that a round block was selected. ### Step 1: Define Events - Let "1" be the event that the first bag is picked - Let "2" be the event that the second bag is picked - Let "3" be the event that the third bag is picked - Let "R" be the event that a round block is drawn ### Step 2: Apply Bayes' Theorem We want: P(2|R) = P(R|2) × P(2) / P(R) ### Step 3: Calculate Individual Probabilities - P(1) = P(2) = P(3) = 1/3 (each bag equally likely to be chosen) - P(R|1) = 2/5 (2 round blocks out of 5 total in bag 1) - P(R|2) = 3/5 (3 round blocks out of 5 total in bag 2) - P(R|3) = 5/5 = 1 (all blocks are round in bag 3) ### Step 4: Calculate Total Probability P(R) 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 ### Step 5: Calculate Final Answer P(2|R) = P(R|2) × P(2) / P(R) = (3/5) × (1/3) / (2/3) = (3/15) / (2/3) = (1/5) / (2/3) = (1/5) × (3/2) = 3/10 Therefore, the probability that the round block came from the second bag is **3/10**.

Author: Tanishq Prabhu