Mathematics part 4 control MPEI
Replenishment date: 12.12.2011
Content: 11212180758027.rar (17.06 KB)
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Description
Test work on the discipline "Mathematics" part 4 "
Task 1.
Casting in blanks for further processing comes from two shops: 70% from the first shop and 30% from the second shop. At the same time, the material of the 1st workshop has 10% scrap, and the material of the 2nd workshop has 20% scrap. Find the probability that one blank, taken at random, has no defects.
Task 2.
In the tournament there are 10 chess players who have the same chances of any outcome in each meeting (only one for every two participants). Find the probability that any one of the participants will hold all the meetings with a win.
Task 3.
The probability of occurrence of event A in a single trial is 0.75. What is the likelihood that if the challenge is repeated eight times, this event will occur more than 6 times?
Task 4.
To determine the average yield of a field with an area of 1800 hectares, a sample of 1 m2 from each hectare was taken. It is known that for each hectare of the field the variance does not exceed 6. Estimate the probability that the deviation of the average sample yield differs from the average yield throughout the field by no more than 0.25 centners.
Task 5.
Out of a batch of 4000 parts for a sample, 500 were checked. At the same time, 3% were non-standard. Determine the probability that the share of non-standard parts in the entire batch differs from their share in the sample by less than 1%.
Task 6.
The three comrades agreed to meet. The first of them is never late, but he warned that he could come to the meeting with a probability of 0.9. The second will be late with a probability of 0.2, and the third is usually late with a probability of 0.4. What is the likelihood that at least two of your three friends will meet by the appointed date (without delay)?
Task 7.
The probability of occurrence of event A in each of 12 repeated independent tests is P (A) = p = 0.75. Determine the mean and variance of a random variable of the number of occurrences of event A in 12 independent retests.
Task 8
For what number n independent tests is the probability of the inequality fulfillment,
where m is the number of occurrences of event A in these n tests, will exceed 0.9, if the probability of occurrence of event A in a separate test is p = 0.7?
Task 1.
Casting in blanks for further processing comes from two shops: 70% from the first shop and 30% from the second shop. At the same time, the material of the 1st workshop has 10% scrap, and the material of the 2nd workshop has 20% scrap. Find the probability that one blank, taken at random, has no defects.
Task 2.
In the tournament there are 10 chess players who have the same chances of any outcome in each meeting (only one for every two participants). Find the probability that any one of the participants will hold all the meetings with a win.
Task 3.
The probability of occurrence of event A in a single trial is 0.75. What is the likelihood that if the challenge is repeated eight times, this event will occur more than 6 times?
Task 4.
To determine the average yield of a field with an area of 1800 hectares, a sample of 1 m2 from each hectare was taken. It is known that for each hectare of the field the variance does not exceed 6. Estimate the probability that the deviation of the average sample yield differs from the average yield throughout the field by no more than 0.25 centners.
Task 5.
Out of a batch of 4000 parts for a sample, 500 were checked. At the same time, 3% were non-standard. Determine the probability that the share of non-standard parts in the entire batch differs from their share in the sample by less than 1%.
Task 6.
The three comrades agreed to meet. The first of them is never late, but he warned that he could come to the meeting with a probability of 0.9. The second will be late with a probability of 0.2, and the third is usually late with a probability of 0.4. What is the likelihood that at least two of your three friends will meet by the appointed date (without delay)?
Task 7.
The probability of occurrence of event A in each of 12 repeated independent tests is P (A) = p = 0.75. Determine the mean and variance of a random variable of the number of occurrences of event A in 12 independent retests.
Task 8
For what number n independent tests is the probability of the inequality fulfillment,
where m is the number of occurrences of event A in these n tests, will exceed 0.9, if the probability of occurrence of event A in a separate test is p = 0.7?