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Diploma Engineering Mathematics

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Published in: Mathematics
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This note contains Important Questions.

Hari B / Hyderabad

9 years of teaching experience

Qualification: M.Sc (jntuh campus - 2012)

Teaches: Algebra, Business Mathematics, Mathematics, Statistics, B.Tech Tuition, Polytechnic

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  1. UNIT -4 PROBABILITY SHORT ANSWER QUESTIONS IN PROBABILITY 10 SHORTTYPE 1. State the mathematical definition of probability. 2. A bag contains 5 Black, 7 Red and 3 White balls. Probability that the drawn is red. A ball is drawn at random. Find the 3. If a dice is thrown , what is the probability of getting an even number. 4. A box contains 3 black, 6 white balls. If a ball is drawn at random , what is the probability That it is a white. 5. A boy contains 4 red , 5 black and 6 blue balls. What is the probability that two balls drawn Simultaneously are one red and one black . 6. If a die is thrown , what is the probability of getting, a) An even number b) an odd number 7. Two dice thrown. Find the probability that none of the dice shows number 2. 8. State Addition and Multiplication Theorems of probanility for two events. 9. An integer is picked from 1 to 20 numbers, both inclusive. Find the probability that it is a Prime. 10. Compute p(A/B), if and P(An B) = 0.32. 11. When two dice are thrown , find the probability of obtaining the total score 7. 12. state the addition theorem on probability. If A and B are mutually independent events such That and then find U B) . 13. WRITE the probability of getting 53 Sundays in a leap year. LONG ANSWER QUESTIONS IN PROBABILITY
  2. 1. A class consists of 10 boys and 20 girls of which half the boys and half the girls have blue eyes Find the probability that a student chosen at random is a boy or has blue eyes. 2. Explain the following terms a)sample space b)random experiment c)elementary and compound events d)equally likely events 3. IN a class of 60 boys and 20 girls half of the boys and of the girls know cricket . Find the probability of the event that a person selected from the class is either a boy or a girl knowing cricket. 4. Find the probability of getting two queens where two cards are draw from a pack of 52 cards. 5. Among 150 students 80 are studying maths , 40 are studying physics and 30 are studying maths And physics. If a student is choosen at random , Find the probability that the student , a)studying maths or physics. b) studying neither maths nor physics B): 0.15 THEN Find B) 6. If U B): 0.65, 7. There are 12 boys and 4 girls in a class If we choose 3 children one after the another in Succession at random 1 find the probability that all the 3 are boys . 8. Let A and B be two events with P(A)= 3/8, P(B) = 5/8, and P(A U B) = 3/4. Find P(A/B) AND P(B/A) 9. Let A and B be two events with P(A) = 3/5, Are A and B are independent . and 3/10, Find P(An B): 1/5. 10. If A and B are independent events with P(A)=O.2 X, and P(A U B) = 0.8, then find 11. WHEN four coins are tossed simultaneously, write the probability of getting 2 heads and 2 tails .
  3. 12. When two dice are thrown, find the probability of getting a sum even number. 13. In a committee of 25 memberes, each member is proficient either in mathematics or in Statistics or in both. If 19 of these are proficient mathematics, 16 in statistics. Find the Probability that a person selected from the committee is proficient in both. 14. when two dice are thrown, find the probability of getting a sum 7. 15. In a hostel 60% students Telugu news paper, 40% students read English news paper and 20% read both the papers. A student is selected at random, find the probability that the Student reads neither telugu nor English news paper. 16. Let A and B be two events with P(A) = 1/2 , B) = 1/3 and P(A n B) = 1 /4 Find i) P(A/B) iii) p(AUB) 17. If and 1/5, FIND n B) If A and B are independent events. 18. If 4 English, 5 drawing , 6 mathematics books are arranged in a shelf in one row, then find The probability that the books of same kind are side by side. 19. A speaks truth in 80% of cases and B in 60% cases. Find the percentage of the cases of Which they likely to contradict each other in stating the same fact. 20. four boys and four girls sit in a row at random . Find the probabilities that i) The girls sit together and ii) boys and girls sit alternately. 21. A given problem is solved by thre students independently with probabilities 0.4 , What is the probability that a given problem is solved? 22. state and prove addition theorem of probability ESSAYS TYPE 0.5, 0.25. 1. Find the probability of drawing 2 red balls in succession from a bag containing 4 red and 5 black balls when the ball a) Not replaced 2. Let A and B be two events that is drawn first is b)replaced with P(A)= h, 1/3 and Find
  4. a) P(A/B) 3. A Problem is given to the three students A, B and C the chances of their solving the Sum are 1/3, 1/4, 1/5 respectively . Find the probability that the problem will be solved. 4. If P(A) = 3/5, AND P(B) -1/5, Find P(An B). IF A and B are independently events. 5. A speeks truth in 80% of the cases and B in 60% of the cases. Find the percentage of the Cases. Find the percentage of the cases of which they likely to contradict each other in starting The same fact. 6. Three machines A, B and C produce respectively 60%, 30% and 10% of the total no. of Items of a factory. The percentages of defective out put of these machines are Respectively 2%, 3% and 4%. An item is selected at random and is found deflective find The probability that the item was produced by machine C. 7. A box I contains eleven cards numbered 1 to 11, box Il contains seven cards numbered 1 to 7. A box is selected at random and a card is drawn. If the number is even, find the Probability that the card is from box l. 8. A bag contains 6 red , 7 black and 8 blue balls. What is the probability that two balls Drawn simultaneously are one red and one black? 9. Two dice are thrown. Find the conditional probability that two fives occurs, if it is known that The total is divisible by 5. 10. Let A and B are independent events with P(A) = 0.8 and P(B) = 0.4. Find i) P(An B) iii) P (A/ B) 11. Box—I contains 3 red, 4 black balls, Box- Il contains 5 red, 6 black balls. One ball is drawn At random from one of the bags and is found to be red. What is the probability that the Ball is drawn from Box- ll. 12. Let A and B are independent events with P(A) = i) 0.3 and P(B) -0.4 FIND iii) P(A/B)
  5. 13. Box- I contains 8 white, 2 black balls, Box- Il contains 5 white, 5 black balls and Box— Ill Contains 4 white, 6 black balls. A box is selected at random and a ball is drawn from it, What is the probability that the ball is white 14. Bag I contains 3 red and 4 black balls while another Bag Il contains 3 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be red. Find the Probability that it was drawn from Bag ll. 15. A box contains 20 screws , 5 of which are defective . 2 screws are drawn at random. The probability that neither of the 2 screws is defective. 16. Evaluate U B) IF and 17. Define i) addition theorem , ii) multiplication theorem and iii) Conditional probability on probability. Find 18. P(A) = 1/2, P(An B) = 1/4, FIND i) P(A/B), ii) B/ A) and iii) P(AU B) 19. For any events A and B it is given that P(A)= 2/3, P(B) = 3/4 and P(A U B) = 5/6. FIND P(A/B) and P(B/ A). 20. In a game or dice , the player wins if sum of numbers on dice is 6 or 8 Probability of his winning if two dice are thrown at a time? . what is the

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