Control Theory of Probability and matem.statistika

Exercise 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 the 1st workshop is 10% of marriage, and the material of the 2nd workshop - 20% of marriage. Find the probability that the one taken at random pig has no defects.
Task 2.
In the tournament there are 10 players that have the same odds of any outcome in each match (only one for every two people). Find the probability that any one of the participants hold a meeting with all the winnings.
Task 3.
The probability of event A in a separate trial is 0.75. What is the probability that the test is repeated eight times this event is more than 6 times appear?
Task 4.
To determine the average yield of the field area of 1800 hectares in the sample taken at 1 m2 per hectare. It is known that for each hectare of field variance is less than 6. Assess the probability that the deviation of the average yield of a sample is different from the average yield throughout the field no more than 0.25 p.
Task 5.
From 4000 the party details on the sample tested 500. In this case turned out to be 3% of non-standard. Determine the probability that the proportion of non-standard parts in the whole batch is different from their share in the sample of less than 1%.
Task 6.
Three friends have agreed to meet. The first of these is never late, but warned that it could come to the meeting with a probability of 0.9. The second late with probability 0.2, and the third is usually late with a probability of 0.4. How likely is it that the appointed time (without delay) will meet at least two of the three friends?
Task 7.
The probability of event A in each of the 12 repeated independent trials P (A) = p = 0.75. Determine the mean and variance of the random variable number of occurrences of A in 12 independent repeated trials.
Task 8
 At what number n independent trials the probability of the inequality,
where m - number of occurrences of A in these n trials, exceeds 0.9, if the probability of the event A in a separate test, p = 0.7?