How to correct a controversial question about probability theory in postgraduate entrance examination?

The mistake of the first method is that the probability of two boxes is 1/2. In the case that the first part is first class, the probability of two boxes is not 1/2.

In fact, the first part is that the first-class product comes from two sources: box 1 and box 2, and the probabilities are10/50/(150+18/30) and18/30/(/) respectively.

Bring these two probabilities into the formula of the first method: 0.25*9/49+0.75* 17/29.

The answer is 0.4855.

Probability theory is a branch of mathematics that studies the quantitative laws of random phenomena. Random phenomenon is relative to decisive phenomenon, and the inevitable occurrence of a certain result under certain conditions is called decisive phenomenon. For example, at standard atmospheric pressure, when pure water is heated to 100℃, water will inevitably boil.

Random phenomenon means that under the same basic conditions, before each experiment or observation, it is uncertain what kind of results will appear, showing contingency. For example, when you flip a coin, there may be heads or tails.

The realization and observation of random phenomena are called random experiments. Every possible result of random test is called a basic event, and a basic event or a group of basic events is collectively called a random event, or simply called an event. Typical random experiments include dice, coins, playing cards and roulette. The probability of an event is a measure of the possibility of an event. Although the occurrence of an event in random testing is accidental, those machine tests that can be repeated in large quantities under the same conditions often show obvious quantitative laws.