Provide proper statements related to the events.

Q21. A company selected engineers through campus interview from a university. Out ofthe total selection made 60%, 30% and 10% are from Electronics, Computer and Mechanical respectively. If 9%, 20% and 60% of the selected students do not join the company. What is the probability that do not join is from computer stream.

Q22. From a vessel containing 3 white and 5 black balls, 4 balls are transferred into an empty vessel. From this vessel a ball is drawn and is found to be white. What is the probability that out of four balls transferred 3 are white and 1 black?

Q23. Mathematics problem is given to three students A1, A2 and A3 , whose chances of solving it are 1/3, 2/5 and 3/7 .What is the probability that the problem will be solved.

Q24. Three students appear at an examination of Physics. The probability of their success are 1/3, 1/4 and 1/5. What is the probability of success at least two?

Q25. From a lot of 25 items containing 5 defective, a sample of 4 items was drawn at random

(i) without replacement (ii) with replacement. Find the probability for selecting two defective each case.

Q26. The chance that a doctor will diagnose a disease correctly is 70% . The chances of death of a patient after current diagnosis is 35%. While after wrong diagnosis it is 80% . If patient dies after taking his treatment, find the probability that he was diagnosed

(i) Wrongly (ii) Correctly.

Q27. For a certain binary Communication channel, the probability that a transmitted 'O' is received as 'O' is 0.95 and the probability that a transmitted '1' is received as '1' is 0.90. If the probability that a 'O' is transmitted is 0.4, find the probability that

(a) a '1' is received . (b) a '1' is transmitted given that a '1' is received .

Q28. A box of fuses contains 20 fuses, of which 5 are defective. If 3 of the fuses are selected at random and removed from the box in succession without replacement, what is the probability that all three fuses are defective?

Q29. 20 tickets are numbered from 1 to 20. One ticket is drawn at random out of these tickets. Find the probability that the ticket number is a multiple of 2 or 5.

Q30. The probability that teacher will give a unannounced test on any day is 1/5. If a student is absent twice, what is the probability that he will miss at least one test.