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Download "Урок 6. Теория вероятности. Правило суммы и произведения вероятности. Алгебра 11 класс."

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задачи про стрелков
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правилосуммы
теориявероятности
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алгебра11класс
высшаяматематика
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  • ruRussian
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00:00:00
hello, the topic of today's lesson
00:00:04
is the sum theorem and the theorem of the product of the
00:00:07
probability of independent events, if both
00:00:12
are not a joint independent event,
00:00:15
then the probability that
00:00:18
either a or b will happen is calculated as the sum of
00:00:22
the probabilities, the probability that both
00:00:25
events a and event b will happen
00:00:28
is calculated as the product
00:00:31
of the probabilities now you can put
00:00:36
pause the video and write down this
00:00:38
rule
00:00:45
example example 1 plant produces 15
00:00:51
percent of premium products 25
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percent of first grade products 40
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percent of products 2 sword everything
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else is defective find the probability
00:01:05
that the product is chosen at random will not be
00:01:07
defective that we have a probability of choosing a
00:01:12
premium product 15 hundredths of the
00:01:15
first grade 25 hundredths of the second grade 40
00:01:19
days
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we need to choose either the highest grade or the
00:01:24
first grade or the second joint if the elite
00:01:29
we put a plus sign added up we counted the
00:01:36
second example at a
00:01:41
shooting competition the shooter hits the top ten with a
00:01:43
probability of 0.4
00:01:46
nine with a probability of 0.1 and into the eight
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with a probability of 0.2
00:01:54
what is the probability that with one
00:01:57
shot the shooter will score the first at
00:02:00
least 9 points at least 9 points this
00:02:04
means that we are satisfied with hitting a
00:02:07
ten or hitting a nine or that
00:02:12
plus added up counted the second at least
00:02:19
eight points at least eight this means
00:02:22
we are satisfied with autumn 910 added up
00:02:27
I will count 3 less than 8 points here you can
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pause the video again and immediately
00:02:40
write down this rule that the probability of
00:02:43
an event the probability of an event
00:02:45
opposite to
00:02:47
the sum is given one you what do we have in the
00:02:55
third case when there are less than 8 points
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we are not satisfied with the probability of getting
00:03:01
into the top ten nine and eight, so
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we subtract this probability from one;
00:03:16
another example: they throw 2 dice,
00:03:19
what is the probability that I get 2
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ones?
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times
00:03:43
what is the probability that a six
00:03:45
will come up only for the second time that for us the
00:03:50
first time we are satisfied with everything except a
00:03:53
six
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the probability that
00:03:57
anything except a six will come out five-sixths the
00:04:01
second time a six should fall out the
00:04:04
probability that a six will fall out
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1 6
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we need it to happen and the first
00:04:13
event and the second, therefore we multiply their
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probabilities
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the following example, the entrance exam
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consists of round 3, the
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probability of dropping out in the first round
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is 60 percent in the second 40
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percent the third 30 percent what is
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the probability of admission to the lyceum
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that in order to enter the lyceum we must
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pass the first round and the second round and the
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third round, the probability of passing the first round is
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40 percent, the second round is 60
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percent, the third round is 70 percent, and
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since we need to pass both 1 and 2 and 3, we
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multiply these probabilities,
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another example, 3 the arrows are independent of each
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other, they shoot once target
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hit probability 1 72 83 60 what is
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the probability that it was the first three
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hits
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three hits this means hit and 1 and 2 and
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3 multiplied these probabilities we got the
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answer 2 3 misses what do we need to
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miss and 1 and 2 and 3 got the
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answer and 3
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find the probability that there was exactly
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one hit, that here if 1 hit, then the
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second third should miss, or
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if 2 hit before 1 and 3 should
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miss, or if the third hit, then the
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first 2 should
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not miss, so we
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multiply the probability of hitting 1 by the probability of
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missing 2 and 3 or sign plus the probability of a
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knife hitting 2 on a miss probability
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1 and 3 or plus the probability of a knife hitting 3
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on a miss probability 1 2
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next example a
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coin is tossed 8 times
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find the probability that a
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coat of arms will appear at least once if our condition
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says at least one then the probability of a
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given event is found using this
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formula, that is, from the total probability from
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one we subtract the only
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result that we are not keen on in this
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case, that we are not satisfied, we are not satisfied
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that all eight times in a row
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it will be heads,
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so we subtract from one the
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probability that eight times it
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will come up heads in a row, you can
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pause the video again and write down this
00:07:50
rule
00:08:00
and another example: two students
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solve one problem independently of each other, the
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first student can solve this problem with a
00:08:10
probability of nine-tenths 2 with a
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probability of 70,
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find the probability that both
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students are first solving the problem here everything is simple and the
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first and second must solve multiplied the
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second
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none of the students by solve the problem the
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same probability of error of the first
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multiplied by the probability of error 2 3
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at least one of the students solve the problem
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again if there is a phrase although it seems to be
00:08:44
from one we take away the only
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option
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that does not suit us, we are not
00:08:51
satisfied with the option that both will be wrong at the same time
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and the fourth, only one of
00:09:00
the students will solve the problem, what do we have if the first one
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decides 2
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will be wrong or if he decides 2 to 1 will be wrong
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and the USA example the store supplies Dremov to
00:09:15
the plant with the products of the first plant this is 40
00:09:18
percent 2 30 percent and 80
00:09:22
percent of the products of the second plant are of the
00:09:24
highest grade,
00:09:25
what is the probability of buying a product of the
00:09:28
second plant of the Supreme Court what we
00:09:31
need we need to buy a product of both the second
00:09:34
plant and the highest grade
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if and then we multiply multiplied we calculated we
00:09:42
got the answer and the last example 7
00:09:48
Strelkov at the same time independent
00:09:50
of each other they shoot bend the probability
00:09:53
of hitting each shooter is 0.8 the
00:09:56
target is hit in one
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hit find the probability of hitting the
00:10:01
target
00:10:03
that our target will be hit if
00:10:07
at least one plow hits if
00:10:11
at least one is there and from one we subtract the
00:10:14
probability that all seven will miss,
00:10:17
that is, once again the task is at least one magician
00:10:22
and one, we take away the only
00:10:24
probability that does not suit us and the
00:10:34
task for independent solution
00:10:37
will be 16 tasks in total for 2 slides, here are the
00:10:41
first 8
00:10:53
and also autumn
00:11:09
the task to make written notebooks for
00:11:12
today, all
00:11:14
good mood, have a good day and
00:11:17
good luck in studying mathematics
00:11:19
thank you it was the season nko moon

Description:

Теория вероятности. Теорема сложения вероятности независимых событий. Теорема умножения вероятности независимых событий. Правило суммы вероятности несовместных независимых событий. Правило произведения вероятности несовместных независимых событий. Теоремы сложения и умножения вероятности несовместных событий. Примеры с решением. Пример 1: Завод выпускает 16% продукции высшего сорта, 24% — первого сорта, 48% — второго сорта, а все остальное — брак. Найти вероятность того, что наугад выбранное изделие не будет бракованным. Пример 2: На соревнованиях по стрельбе стрелок попадает в десятку с вероятностью 0,03, в девятку — 0,2, в восьмерку — 0,3. Какова вероятность того, что одним выстрелом стрелок наберет: 1) больше восьми очков; 2) меньше восьми очков; 3) не меньше восьми очков? Пример 3: В коробке лежат 4 голубых, 3 красных, 9 зеленых, 6 желтых шариков. Из коробки наугад взяли один шарик. Какова вероятность того, что этот шарик будет не зеленым? Пример 4: Бросают два игральных кубика. Какова вероятность того, что выпадут две шестерки? Пример 5: Бросают два игральных кубика. Какова вероятность того, что выпадут две нечетные цифры? Пример 6: Бросают три монеты. Какова вероятность того, что выпадут две цифры и герб? Пример 7: Игральный кубик бросают три раза. Какова вероятность того, что шестерка выпадет только во второй раз? Пример 8: Магазин снабжается тремя молокозаводами. Продукция первого завода составляет 60%, второго — 20%, причем 90% продукции первого завода высшего сорта. Какова вероятность покупки продукта первого завода высшего сорта? Пример 9: Три станка изготовляют соответственно 50%, 40%, 10% всех изделий. В их работе брак соответственно составляете 1%, 2%, 4%. Какова вероятность того, что взятое наугад изделие будет бракованным? Пример 10: Три стрелка независимо друг от друга по одному разу стреляют в цель. Вероятность попадания первого стрелка составляет 0,6, второго — 0,8, третьего — 0,7. Какова вероятность того, что было: 1) три промаха; 2) хотя бы одно попадание; 3) ровно два попадания? Пример 11: Монету подбрасывают десять раз. Найти вероятность того, что хотя бы один раз выпадет цифра. Пример 12: Два ученика независимо друг от друга решают одну задачу. Первый ученик может решить эту задачу с вероятностью 0,8, а второй — 0,9. Найти вероятность того, что: 1) оба ученика решат задачу; 2) ни один из учеников не решит задачу; 3) хотя бы один из учеников решит задачу; 4) только один из учеников решит задачу. Пример 13: Пять стрелков одновременно независимо друг от друга стреляют в одну цель. Вероятность попадания каждого стрелка равна 0,7. Поражение цели происходит за одно попадание. Найти вероятность поражения цели. Математика. Алгебра 11 класс. Решение заданий с объяснением. Видеоуроки по математике. Устранение пробелов в знаниях по математике. Подготовка к ЗНО ( ВНО ) по математике. Подготовка к ЕГЭ, ДПА ( ГИА ), ОГЭ по математике.

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