Reference no: EM132852358
Task 1. Can the sum of two events A and B coincide with their product?
Task 2. Event B is a part of event A, i.e. from the appearance of event B with certainty follows the appearance of event A. What are: their sum; their product?
Task 3. The probabilities of two incompatible (unjointed) and independent events A and B are known: P (A) = 0,2; P (B) = 0,6. Find:
?) P(?+?); b) P(??); c) P(?/?).
Task 4. Over the manufacture of the product consistently k workers; the quality of the product during the transfer to the next worker is not checked. The first worker admits marriage with probability p1, the second p2 and so on. Find the likelihood that the manufacture of the product will be defective.
Task 5. In the urn of a white and b black balls. A ball is taken out of the urn at random, its color is marked, and the ball returns to the urn. After that, another ball is taken from the urn. Find the likelihood that both balls drawn out will be white.
Task 6. In the urn of a white and b black balls. Two balls are taken out at random (simultaneously or sequentially) from the urn. Find the probability that both balls will be white.
Task 7. Toss two coins. Events are considered: A - emblem on the first coin; B - emblem on the second coin. Find the probability of the event C = A + B.
Task 8. Rolling pair dice. What is the probability that the sum of points on upper sides will not be more than 6?
Task 9. Among 100 lottery tickets there are 5 winning ones. Find the probability that 2 selected tickets will be winning.
Task 10. Each of the four mutually exclusive events can occur with probabilities of 0.012, 0.010, 0.006, and 0.002, respectively. Find the probability that at least one of these events will occur as a result of the experiment.
Task 11. Two shooters independently shoot one shot at a target. The probability of hitting the target with the first shooter is 0.8, and the second is 0.9. Find the probability of hitting the target?
Task 12. The studio has three television cameras. The probability that each camera is turned on at the moment is 0.6. Find the probability that at least one camera is currently turned on.
Task 13. For the manufacture of parts requires three basic operations. The probability of a defect in the first operation is 0.01, in the second - 0.02, in the third - 0.025. Find the probability of manufacturing a standard part, provided that the appearance of marriage in certain operations is independent.
Task 14. The workshop produces on average 2% of defective parts. Out of every hundred standard parts, on average 70 are first-class. Find the probability that the part manufactured in the workshop will be of the first grade.
Task 15. When transmitting text, 10% of the letters are distorted and received incorrectly. What is the likelihood that all five letters of a given word will be accepted correctly?