Problem Breakdown:

1. On any one day:

   • The average number of days it rains per week is 6.
   • There are 7 days in a week.
   • The probability $P(\text{rain on one day})$ is simply the ratio of the number of rainy days to the total number of days: $P(\text{rain on one day}) = \frac{6}{7}$

2. On two successive days:

   • To find the probability that it rains on two consecutive days, we assume that the events are independent (i.e., whether it rains on one day does not affect the probability for the next day).
   • Therefore, the probability $P(\text{rain on two successive days})$ is the product of the probabilities for each day: $P(\text{rain on two successive days}) = P(\text{rain on one day}) \times P(\text{rain on one day}) = \frac{6}{7} \times \frac{6}{7} = \frac{36}{49}$

3. On three successive days:

   • Similarly, the probability $P(\text{rain on three successive days})$ is the product of the probabilities for each of the three days: $P(\text{rain on three successive days}) = P(\text{rain on one day}) \times P(\text{rain on one day}) \times P(\text{rain on one day}) = \left( \frac{6}{7} \right)^3 = \frac{216}{343}$

Final Answer:

• Probability of rain on one day: $\frac{6}{7}$
• Probability of rain on two successive days: $\frac{36}{49}$
• Probability of rain on three successive days: $\frac{216}{343}$

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Would you like more details or have any questions?

Here are 5 relative questions that could expand this concept:

1. What is the probability that it doesn't rain on any given day?
2. How would the probability change if the average number of rainy days per week decreases?
3. What is the probability of having rain on four successive days?
4. How do we calculate the probability of rain for any non-consecutive days in a week?
5. What would the probability be if there were unequal chances for rain on different days?

Tip: When calculating successive event probabilities, always multiply individual event probabilities if they are independent.