Examination in Mathematics MEI Part 4

Task 1.
Casting into blanks for further processing comes from two workshops: 70% of the first workshop and 30% from the second shop. This material is 1-Gro plant has a 10% marriage, and the material of the 2nd workshop - 20% of marriage. Find the probability that the one taken at random disc is not defective.


Task 2.
In the event there are 10 players with the same chances of any outcome in every meeting (only one for every two people). Find the probability that any one of the participants will win all the meetings c.


Task 3.
The probability of occurrence of an event and a separate test is 0.75. What is the likelihood that the eightfold repetition of the test event will be more than 6 times?

Task 4.
To determine the average yield of the field area of \u200b\u200b1800 hectares in the sample taken at 1 m2 per hectare. It is known that for every hectare field variance is less than 6. Assess the probability that the deviation of the average yield of a sample differs from the average yield for the whole field of no more than 0.25 p.

Task 5.
From 4000 the party details on the sample tested 500. This turned out to 3% of non-standard. Determine the probability that the proportion of non-standard parts in the whole Party is different from their share in the sample of less than 1%.

Task 6.
Three friends agreed to meet. The first of them never late, but warned that he could come to the meeting with a probability of 0.9. Second chance late 0.2, while the third is usually late with probability 0.4. What is the probability that the appointed time (without delay) will meet at least two of the three friends ?.

Task 7.
The probability of occurrence of an event A in each of the 12 independent repeated tests Determine the mean and variance of the number of occurrences of A in 12 independent repeated tests.

Task 8.
At what number n independent trials probability of the inequality, where m - the number of occurrences of A in n trials, exceeds 0.9, if the probability of occurrence of an event and in some test?