Simple probability problem

There is no problem with the topic. When solving the probability problem again, we should first find out the events, then find out the relationship between the events, and then calculate according to the corresponding formulas (such as multiplication formula and addition formula).

0.6*0.3 is not equal to 0. 1, indicating that the two events are not independent.

By the way, show the landlord an example (an exercise in a college textbook)

In order to prevent accidents, two sets of alarm systems, A and B, were installed in the mine. Each system is used independently, and the successful alarm is 0.92 for A and 0.93 for B; In the case of failure, the probability of B's successful alarm is 0.85. Find the probability of alarm success in case of B fault.

When solving this problem, whether they are independent or not is completely irrelevant, because it is impossible to see from the topic, and it is ok to calculate directly by formula.

A# doesn't happen to A, and B# doesn't happen to B.

P(a)=0.92 P(b)=0.93 P(b/a#)=0.85 This is a known topic.

Then p (b #/a #) =1-p (b/a #) = 0.15.

P(a # b #)= P(a #)* P(b #/a #)= 0.08 * 0. 15 = 0.0 12

Then p (a #/b #) = p (a # b #)/p (b #) = 0.012/0.07 = 6/35.

The final answer is P(a/b#)= 1-6/35=29/35.

Therefore, it is not necessary to be too independent to do probability questions, and it can be calculated according to known conditions.