ENGINEERING PROBABILITY

ENGINEERING PROBABILITYQ1. Compute the mean, median, mode and sample standard deviation of the following set of numbers: 2, 4, 6, 8, 10, 12.Q2. Out of 40 students, 14 are taking English composition and 29 are taking Chemistry. (a) If 5 students are in both classes, how many students are in neither class? (b) How many are in either class? (c) What is the probability that a randomly-chosen student from this group is taking only the Chemistry class?

Q3. A survey at a US hospital showed the most popular names for baby girls are: Emily, Haley, Kayla and Samantha. The most popular middle names for baby girls are Anne, Elizabeth and Marie. How many possible names can be generated using the first and middle names from the list of popular names? A. 12B. 16C. 24D. 26

Q4. How many 3-digit numbers may be formed from the digits 0, 1, 2, 3, 4 & 5 ifno digit may be repeated in a given number.How many of these are odd?How many of these are even?

Q5. There are 8 flags of different colors. Any arrangement of 5 of them in a row constitute a signal. (a) How many signals can be made? (b) If one of the flags is red, how many signals can be made if each signal includes the red flag? Q6. In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?Ans. 72Q7. In how many ways can 6 persons be seated around a table with 6 chairs (a) if they can sit anywhere? (b) if two individuals wanted to be seated side by side? (c) if two individuals must not sit next to each other? Q8. A bag contains 4 red balls , 3 white balls and 9 blue balls. Find: (a) the no. of ways of drawing any 3 balls; (b) the no. of ways of drawing 3 red balls; (c) the no. of ways of drawing 3 balls such that 2 are white and one is blue.

Q9. In how many ways can you invite one or more of five friends to a party?A. 25B. 15C. 31D. 62Q10. Assuming equal probabilities for boys and girls, find the probability in families with 3 children that (a) all are boys, (b) there are two girls and one boy.

Q11. A pair of dice is tossed. Find the probability that the sum of the numbers coming up is less than 11.

Q12. Each of the first 9 letters of the alphabet and each of the first 9 positive integers is written on a separate slip of paper. These slips, which are identical, are placed in a box and thoroughly mixed. What is the probability, in a single draw, of obtaining either a vowel or an odd integer?

Q13. A card is drawn from a deck of 52 cards. Find the probability of drawing a king or a red card.

Q14. A pair of dice is thrown. If it is known that one die shows a 4, what is the probability that the other die shows a 5?

Q15. A card is drawn from a deck of 52 cards and then a second card is drawn. Find the probability that the first card is a spade and the second a club if (a) the first card is replaced before the second card is drawn, (b) if the first card is not replaced.

Q16. In a certain assembly plant, three machines, B1, B2, and B3, make 30%, 45%, and 25%, respectively, of the products. It is known from past experience that 2%, 3%, and 2% of the products made by each machine, respectively, are defective. Now, suppose that a finished product is randomly selected, what is the probability that it is defective? Ans. 0.0245

Q17. During a board examination, there were 350 examinees from Luzon, 250 from the Visayas and 400 from Mindanao. The results of the exam revealed that the flunkers from Luzon, Visayas and Mindanao were 3%, 5% and 7% respectively. If the name of a flunker is picked at random, what is the probability that he/she is from Mindanao?0.330C. 0.5490.42D. 0.375

Q18. At a certain intersection, the light for eastbound traffic is red for 15 seconds, yellow for 5 seconds, and green for 30 seconds. Find the probability that out of the next eight eastbound cars that arrive randomly at the light, exactlythree will be stopped by a red light. Ans. 0.254Q19. A coin is biased so that a head is twice as likely to occur as a tail. If it is thrown three times, find the probability of having at least 2 heads. 2/3C. 20/2719/27D. 7/9

Q20. Find the probability that a person tossing three coins will get either all heads or all tails for the second time on the fifth toss.Ans. 27/256Q22. If 7 cards are dealt from an ordinary deck of 52 playing cards, what is the probability that exactly 2 of them will be face cards? Ans. 0.3246

Q23. If a pair of dice are tossed 6 times, what is the probability of obtaining a total of 7 or 11 twice, a matching pair once, and any other combination 3 times? Ans. 0.1127

Q24. On the average a certain intersection results in 3 traffic accidents per month. What is the probability that in any given month exactly 5 accidents will occur at this intersection?Ans. 0.1008

Mathematical Expectation This is what you would expect the outcome of an experiment to be on the average.Q25. In making 100 draws from an ordinary deck of cards (replacing the card drawn before making the next draw), what is the expected no. of times that a heart is drawn?

Q26. In a gambling game, a man is paid $5 if he gets all heads or all tails when three coins are tossed and he pays out $3 if either one head or two heads show. What is his expected gain?

Q27. The number of adults living in homes on a randomly selected city block is described by the following probability distribution:

(a) What is the probability that 4 adults reside at a randomly selected home?(b) What is the mean (or expected value) of the distribution?

No. of adults, X1234Probability P(X)0.250.50.15?