1. Events that will inevitably occur under certain conditions;
Call it an inevitable event;
2. Events that cannot happen under specific conditions;
Called the impossible event;
3. Events that may or may not occur under specific conditions;
It is called a random event.
4. Probability of random events
5. Probabilistic properties of random events
1)0≤P(A)≤ 1，
2) The probability of an impossible event is 0,
The probability of an inevitable event is 1,
The probability of random events is greater than 0 and less than 1.
For random events, do we only
Can be found through a large number of repeated experiments.
What are the odds?
Can a large number of repeated experiments be avoided in some cases?
For example, if you toss a uniform coin, the possible results are: heads up and tails up.
This is consistent with the results of a large number of repeated experiments.
For example, when a dice is rolled, the upward number when it lands may be ... it may be one of 1, 2, 3, 4, 5, 6.
This analysis is also consistent with the results of a large number of repeated experiments
Is consistent.
In other words, there are six possible outcomes, each of which
The chances of these results are ... equal (because the dice are even).
Equal probability of possible events:
(1) Basic event: Call the test and every possible result.
For a basic event.
For example, the coin toss test consists of two basic events. Throw a uniform
The unified cube toy experiment consists of six basic events.
(2) If a test consists of n basic events, and all the basic events
The probability of occurrence is equal, so the probability of each basic event is
1/n .
(3) If there are n basic events in a test, and all the basic events
The possibility of occurrence is equal, in which event A contains M kinds of results, so
The probability P(A) of event a is m/n(m≤n).
Event A: An event in the experiment, which consists of one or several basic events.
Example 1 To study the germination of maize seeds, a maize was planted in Petri dishes 1, No.2 and No.3. 。
(1) lists all basic events;
(1) According to the order of 1, No.2 and No.3 Petri dishes, the possible results of corn seed germination are: (germination, germination, germination), (germination, germination, no germination),
(germination, no germination, germination), (no germination, germination),
(germination, no germination, no germination), (no germination, no germination),
No germination, no germination, no germination.
* * * There are 23 = 8 basic events.
(2) What basic events constitute the following random events:
Event A: All three grains germinate;
Event B: Just two grains germinated;
Event c: At least one seed germinates.
Example 2. Throw a penny, two cents and five cents at a time,
(1) Write all possible upward results.
(positive, positive, positive), (positive, positive, negative), (positive, negative, positive),
(negative, positive, positive), (positive, negative, negative), (negative, positive, negative),
(anti, anti, positive), (anti, anti, anti).
(2) What is the probability of having two heads 1 tails?
To calculate the probability of an equally probable event:
(3) calculate p (a) = m/n.
(1) Calculate the total result number n of all basic events;
(2) calculating the number m of results contained in event a;