Probability · NDA previous year questions

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2016 25 questions

Q1042016 · 18 Sept 2016
A random sample of 20 people is classified in the following table according to their ages: | Age | Frequency | |---|---| | 15 - 25 | 2 | | 25 - 35 | 4 | | 35 - 45 | 6 | | 45 - 55 | 5 | | 55 - 65 | 3 | What is the mean age of this group of people?
1. A.41.0
2. B.41.5
3. C.42.0
4. D.42.5
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Answer: B
Q1052016 · 18 Sept 2016
A special dice with numbers 1, -1, 2, -2, 0 and 3 is thrown thrice. What is the probability that the sum of the numbers occurring on the upper face is zero?
1. A.1/72
2. B.1/8
3. C.7/72
4. D.25/216
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Answer: D
Q1062016 · 18 Sept 2016
There is 25% chance that it rains on any particular day. What is the probability that there is at least one rainy day within a period of 7 days?
1. A. $1 - (\frac{1}{4})^{7}$
2. B. $(\frac{1}{4})^{7}$
3. C. $(\frac{3}{4})^{7}$
4. D. $1 - (\frac{3}{4})^{7}$
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Answer: D
Q1072016 · 18 Sept 2016
A salesman has a 70% chance to sell a product to any customer. The behaviour of successive customers is independent. If two customers A and B enter, what is the probability that the salesman will sell the product to customer A or B?
1. A.0.98
2. B.0.91
3. C.0.70
4. D.0.49
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Answer: B
Q1082016 · 18 Sept 2016
A student appears for tests I, II and III. The student is considered successful if he passes in tests I, II or I, III or all the three. The probabilities of the student passing in tests I, II and III are m, n and 1/2 respectively. If the probability of the student to be successful is 1/2, then which one of the following is correct?
1. A.m(1 + n) = 1
2. B.n(1 + m) = 1
3. C.m = 1
4. D.mn = 1
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Answer: A
Q1092016 · 18 Sept 2016
Three candidates solve a question. Odds in favour of the correct answer are 5 : 2, 4 : 3 and 3 : 4 respectively for the three candidates. What is the probability that at least two of them solve the question correctly?
1. A.209/343
2. B.134/343
3. C.149/343
4. D.60/343
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Answer: A
Q1102016 · 18 Sept 2016
A medicine is known to be 75% effective to cure a patient. If the medicine is given to 5 patients, what is the probability that at least one patient is cured by this medicine?
1. A. $\frac{1}{1024}$
2. B. $\frac{243}{1024}$
3. C. $\frac{1023}{1024}$
4. D. $\frac{781}{1024}$
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Answer: C
Q1112016 · 18 Sept 2016
For two events, A and B, it is given that $P (A) = \frac{3}{5}$ , $P (B) = \frac{3}{10}$ and $P (A ∣ B) = \frac{2}{3}$ . If $\overline{A}$ and $\overline{B}$ are the complementary events of A and B, then what is $P (\overline{A} ∣ \overline{B})$ equal to?
1. A. $\frac{3}{7}$
2. B. $\frac{3}{4}$
3. C. $\frac{1}{3}$
4. D. $\frac{4}{7}$
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Answer: A
Q1122016 · 18 Sept 2016
A machine has three parts, A, B and C, whose chances of being defective are 0.02, 0.10 and 0.05 respectively. The machine stops working if any one of the parts becomes defective. What is the probability that the machine will not stop working?
1. A.0.06
2. B.0.16
3. C.0.84
4. D.0.94
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Answer: C
Q1132016 · 18 Sept 2016
Three independent events, $A_{1}, A_{2}$ and $A_{3}$ occur with probabilities $P (A_{i}) = \frac{1}{1 + i}$ , $i = 1, 2, 3$ . What is the probability that at least one of the three events occurs?
1. A. $\frac{1}{4}$
2. B. $\frac{2}{3}$
3. C. $\frac{3}{4}$
4. D. $\frac{1}{24}$
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Answer: C
Q1142016 · 18 Sept 2016
A coin is tossed three times. Consider the following events: A : No head appears B : Exactly one head appears C : At least two heads appear Which one of the following is correct?
1. A. $(A \cup B) \cap (A \cup C) = B \cup C$
2. B. $(A \cap B^{'}) \cup (A \cap C^{'}) = B^{'} \cup C^{'}$
3. C. $A \cap (B^{'} \cup C^{'}) = A \cup B \cup C$
4. D. $A \cap (B^{'} \cup C^{'}) = B^{'} \cap C^{'}$
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Answer: D
Q1152016 · 18 Sept 2016
In a series of 3 one-day cricket matches between teams A and B of a college, the probability of team A winning or drawing are 1/3 and 1/6 respectively. If a win, loss or draw gives 2, 0 and 1 point respectively, then what is the probability that team A will score 5 points in the series?
1. A. $\frac{17}{18}$
2. B. $\frac{11}{12}$
3. C. $\frac{1}{12}$
4. D. $\frac{1}{18}$
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Answer: D
Q1162016 · 18 Sept 2016
Let the random variable X follow B(6, p). If 16 P(X = 4) = P(X = 2), then what is the value of p?
1. A. $\frac{1}{3}$
2. B. $\frac{1}{4}$
3. C. $\frac{1}{5}$
4. D. $\frac{1}{6}$
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Answer: C
Q1172016 · 18 Sept 2016
What is $[x y z] a h g h b f g f c$ equal to ?
1. A. $[a x + h y + g z h + b + f g + f + c]$
2. B. $a h x g h b y f g f z c$
3. C. $a x + h y + g z h x + b y + f z g x + f y + cz$
4. D. $[a x + h y + g z h x + b y + f z g x + f y + cz]$
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Answer: D
Q922016 · 17 Apr 2016
A fair coin is tossed 100 times. What is the probability of getting tails an odd number of times?
1. A. $\frac{1}{2}$
2. B. $\frac{3}{8}$
3. C. $\frac{1}{4}$
4. D. $\frac{1}{8}$
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Answer: A
Q932016 · 17 Apr 2016
Three dice are thrown simultaneously. What is the probability that the sum on the three faces is at least 5?
1. A. $\frac{17}{18}$
2. B. $\frac{53}{54}$
3. C. $\frac{103}{108}$
4. D. $\frac{215}{216}$
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Answer: B
Q942016 · 17 Apr 2016
Two independent events $A$ and $B$ have $P (A) = \frac{1}{3}$ and $P (B) = \frac{3}{4}$ . What is the probability that exactly one of the two events $A$ or $B$ occurs?
1. A. $\frac{1}{4}$
2. B. $\frac{5}{6}$
3. C. $\frac{5}{12}$
4. D. $\frac{7}{12}$
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Answer: D
Q952016 · 17 Apr 2016
A coin is tossed three times. What is the probability of getting head and tail alternately?
1. A. $\frac{1}{8}$
2. B. $\frac{1}{4}$
3. C. $\frac{1}{2}$
4. D. $\frac{3}{4}$
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Answer: B
Q962016 · 17 Apr 2016
A card is drawn from a well-shuffled deck of 52 cards. What is the probability that it is queen of spade?
1. A. $\frac{1}{52}$
2. B. $\frac{1}{13}$
3. C. $\frac{1}{4}$
4. D. $\frac{1}{8}$
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Answer: A
Q972016 · 17 Apr 2016
If two dice are thrown, then what is the probability that the sum on the two faces is greater than or equal to 4?
1. A. $\frac{13}{18}$
2. B. $\frac{5}{6}$
3. C. $\frac{11}{12}$
4. D. $\frac{35}{36}$
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Answer: C
Q982016 · 17 Apr 2016
A certain type of missile hits the target with probability $p = 0.3$ . What is the least number of missiles should be fired so that there is at least an $80%$ probability that the target is hit?
1. A.5
2. B.6
3. C.7
4. D.None of the above
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Answer: A
Q992016 · 17 Apr 2016
For two mutually exclusive events $A$ and $B$ , $P (A) = 0.2$ and $P (\overline{A} \cap B) = 0.3$ . What is $P (A ∣ (A \cup B))$ equal to?
1. A. $\frac{1}{2}$
2. B. $\frac{2}{5}$
3. C. $\frac{2}{7}$
4. D. $\frac{2}{3}$
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Answer: B
Q1002016 · 17 Apr 2016
What is the probability of 5 Sundays in the month of December?
1. A. $\frac{1}{7}$
2. B. $\frac{2}{7}$
3. C. $\frac{3}{7}$
4. D.None of the above
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Answer: C
Q1012016 · 17 Apr 2016
A point is chosen at random inside a rectangle measuring 6 inches by 5 inches. What is the probability that the randomly selected point is at least one inch from the edge of the rectangle?
1. A. $\frac{2}{3}$
2. B. $\frac{1}{3}$
3. C. $\frac{1}{4}$
4. D. $\frac{2}{5}$
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Answer: D
Q1022016 · 17 Apr 2016
If $z = x + i y = (\frac{1}{2} - \frac{i}{2})^{- 25}$ , where $i = - 1$ , then what is the fundamental amplitude of $\frac{z - 2}{z - i 2}$ ?
1. A. $π$
2. B. $\frac{π}{2}$
3. C. $\frac{π}{3}$
4. D. $\frac{π}{4}$
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Answer: A