If she wins a colour TV, then what is the probability that candy was from bag 𝐵1B 1​ ? (Enter the answer correct to two decimal places).

To determine the probability that the candy was from bag $B_1$ given that she wins a color TV, we can use Bayes' theorem.

1. Break Down the Problem

Let:

• $A$: event that she wins a color TV.
• $B_1$: event that the candy was from bag $B_1$.

We want to find $P(B_1 | A)$.

2. Relevant Concepts

Bayes' theorem states: $P(B_1 | A) = \frac{P(A | B_1) \cdot P(B_1)}{P(A)}$ Where:

• $P(A | B_1)$ is the probability of winning a TV given that the candy was from bag $B_1$.
• $P(B_1)$ is the prior probability that the candy was from bag $B_1$.
• $P(A)$ is the total probability of winning a TV across all bags.

3. Analysis and Detail

1. Identify values for $P(A | B_1)$, $P(B_1)$, and $P(A)$.
2. $P(B_1)$ needs to be known or assumed based on the distribution of candy among the bags.
3. Calculate $P(A)$ using the total probability law: $P(A) = P(A | B_1) \cdot P(B_1) + P(A | B_2) \cdot P(B_2) + \ldots$

4. Verify and Summarize

Plug in the respective values to compute $P(B_1 | A)$ and ensure all calculations are accurately reflecting the relationships defined. Ensure results are rounded correctly to two decimal places.

Final Answer

The final answer will depend on the specific probabilities provided for each event. Please input the necessary values for $P(A | B_1)$, $P(B_1)$, and others to determine $P(B_1 | A)$ accurately.