# 8. Solution.

Let's find the probability of the opposite event "the groups will not be able to contact each other." Consider pairs of tourists where the first tourist is from the first group and the second is from the second group. There are a total of $6 \cdot 7=42$ such pairs. Therefore, the probability that none of the tourists have a phone number of anyone from the other group is $(1-p)^{42}$.

Thus, the desired probability is $1-(1-p)^{42}$.
Answer: $1-(1-p)^{42}$

| Evaluation Criterion | Score |
| :--- | :---: |
| Solution is complete and correct | 3 |
| Probability of the opposite event is found, last step is missing | 2 |
| Principle of solution is correct, but the number of pairs is calculated incorrectly | 1 |
| Solution is missing or completely incorrect | 0 |

## XI Internet Olympiad in Probability Theory and Statistics. Qualifying Round  Answers and Solutions

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