To solve the problem, we need to determine the probability that a randomly chosen book, which is found to be good, was supplied by Q. We'll use Bayes' theorem to solve this problem.

Given Information:

• Probability that a book is supplied by P, $P(P) = 0.60$
• Probability that a book is supplied by Q, $P(Q) = 0.40$
• Probability that a book supplied by P is good, $P(G | P) = 0.96$
• Probability that a book supplied by Q is good, $P(G | Q) = 0.72$

Required Probability:

We need to find the probability that a book was supplied by Q given that it is good, i.e., $P(Q | G)$.

Applying Bayes' Theorem:

$P(Q | G) = \frac{P(G | Q) \cdot P(Q)}{P(G)}$

Where $P(G)$ is the total probability that a book is good, which can be calculated as: $P(G) = P(G | P) \cdot P(P) + P(G | Q) \cdot P(Q)$

Substituting the given values: $P(G) = (0.96 \times 0.60) + (0.72 \times 0.40)$

Now, let's calculate $P(G)$: $P(G) = (0.576) + (0.288) = 0.864$

Calculate $P(Q | G)$:

$P(Q | G) = \frac{0.72 \times 0.40}{0.864} = \frac{0.288}{0.864} = \frac{1}{3} \approx 0.333$

Final Answer:

The probability that a randomly chosen book, which is found to be good, was supplied by Q is approximately 0.333 or 33.3%.

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Do you want more details on this or have any questions?

Here are five related questions:

1. How would the probability change if Q supplied 50% of the books?
2. What is the probability that a randomly chosen book was supplied by P and is good?
3. How would you approach if Q’s books had a different good percentage?
4. What is the probability that a randomly chosen book is bad?
5. How does Bayes' theorem help in real-world decision-making?

Tip: Bayes' theorem is crucial in updating probabilities based on new information, making it highly applicable in fields like diagnostics and machine learning.