4. (10 points) In a lottery, 6 numbers out of 36 are drawn each week. What is the probability that at least one of the numbers drawn this week will be the same as one of the numbers drawn last week? Round the result to the nearest thousandth.
Answer: 0.695

Solution. Total outcomes: $C_{36}^{6}$; outcomes in which no number matches: $C_{30}^{6}$. Then the probability is $1-\frac{C_{30}^{6}}{C_{36}^{6}}$.