The probability of rain in Mumbai on 10th June is 0.6 and the probability that it will rain on
the 10th and 11th June is 0.3. Given that it rained on the 10th of June of a certain year, what
is the probability that it will rain on 11th June?

The problem requires calculating the conditional probability that it will rain on the 11th of June, given that it rained on the 10th of June. Let's denote the events as follows:

- \( A \): It rains on the 10th of June.
- \( B \): It rains on the 11th of June.

We are given:
- \( P(A) = 0.6 \) (Probability that it rains on the 10th of June).
- \( P(A \cap B) = 0.3 \) (Probability that it rains on both the 10th and 11th of June).

We need to find \( P(B \mid A) \), the probability that it rains on the 11th given that it rained on the 10th.

The formula for conditional probability is:

\[
P(B \mid A) = \frac{P(A \cap B)}{P(A)}
\]

Substituting the given values:

\[
P(B \mid A) = \frac{0.3}{0.6} = 0.5
\]

So, the probability that it will rain on the 11th of June given that it rained on the 10th of June is **0.5**.

Would you like more details or have any questions?

Here are five related questions:
1. What is conditional probability, and how is it used in real-life scenarios?
2. How do you calculate the probability of independent events?
3. Can the probability of rain on consecutive days be independent?
4. How does Bayes' theorem relate to conditional probability?
5. What is the significance of the intersection of events in probability theory?

**Tip:** Always ensure that the events are clearly defined and that you use the correct formula for the situation, such as conditional probability or joint probability, depending on the context.

Calculate the conditional probability of rain in Mumbai on June 11th given that it rained on June 10th. Understand how to apply conditional probability in real-life weather scenarios.

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