It is known from the past experience that in a certain plant, there are on an average 4 industrial accidents per month. Find the probability that in a given year, there will be less than 4 accidents.

The probability of a 25-year-old and another 35-year-old living together for 10 years is 0.6. What is the probability that a 30-year-old person will die within 15 years, if it is known that 4000 people out of 54000 at 25 years old will die before reaching the age of 30?

From observations of the weather, it is known that on October 20 the probability of rain is 0.85. A certain forecast method for October 20 is correct  0.9 times if rain is predicted and 0.75 times if no rain is predicted.  How much information does a real weather forecast provide 20 th of October?

On average there are 3 leaks for every 100 miles of a pipeline. What is the probability that a 50-mile section of the pipeline has at least 1 leak?