In the whole length, the number of basic events is infinite, and so is the number of basic events of an event. At this point, the probability of finding an event is generally converted into a ratio of lengths.

Example 1 Take a 3-meter-long rope, straighten it and cut it at any position. What is the probability that the length of the cut two segments is not less than 1 m?

Solution: Remember that it is an event to cut two lengths of rope not less than 1 m, and divide the rope into three equal parts, so when the cutting position is in the middle, the event will occur. Since the length of the middle section is equal to the length of the rope, the probability of the event is 1/3.

Second, the problem of area and region.

Example 2 Two people meet at 18: 00 to 19: 00. The person who comes first must wait for the person who is late for 40 minutes before leaving. If two people set out independently, the probability of meeting at each time from 18: 00 to 19: 00 is equal, and the probability of meeting within the agreed time is found.

Solution: Let two people arrive at the appointment place at and respectively, so that they can meet within the agreed time range and only | x-y |

Third, the problem of space volume.

Example 3 What is the probability that a seed with wheat rust is mixed with a high-yield wheat seed and taken out at random?

Analysis: the distribution of diseases in this seed can be regarded as random, the obtained seed can be regarded as the area that constitutes the event, the seed can be regarded as the area that consists of all the results of the experiment, and the probability can be calculated by the "volume ratio" formula.

Solution: Take out the seeds, in which the event "Seeds contain wheat rust" is recorded as, then the probability =10/1000 = 0.1.