Probability · NDA previous year questions

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2015 23 questions

Q1062015 · 27 Sept 2015
Three digits are chosen at random from 1, 2, 3, 4, 5, 6, 7, 8 and 9 without repeating any digit. What is the probability that the product is odd?
1. A. $\frac{2}{3}$
2. B. $\frac{7}{48}$
3. C. $\frac{5}{42}$
4. D. $\frac{5}{108}$
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Answer: C
Q1072015 · 27 Sept 2015
Two events $A$ and $B$ are such that $P (not B) = 0.8$ , $P (A \cup B) = 0.5$ and $P (A ∣ B) = 0.4$ . Then $P (A)$ is equal to
1. A.0.28
2. B.0.32
3. C.0.38
4. D.None of the above
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Answer: C
Q1082015 · 27 Sept 2015
If mean and variance of a Binomial variate $X$ are 2 and 1 respectively, then the probability that $X$ takes a value greater than 1 is
1. A. $\frac{2}{3}$
2. B. $\frac{4}{5}$
3. C. $\frac{7}{8}$
4. D. $\frac{11}{16}$
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Answer: D
Q1092015 · 27 Sept 2015
Seven unbiased coins are tossed 128 times. In how many throws would you find at least three heads?
1. A.99
2. B.102
3. C.103
4. D.104
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Answer: A
Q1102015 · 27 Sept 2015
A coin is tossed five times. What is the probability that heads are observed more than three times?
1. A. $\frac{3}{16}$
2. B. $\frac{5}{16}$
3. C. $\frac{1}{2}$
4. D. $\frac{3}{32}$
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Answer: A
Q1112015 · 27 Sept 2015
An unbiased coin is tossed until the first head appears or until four tosses are completed, whichever happens earlier. Which of the following statements is/are correct? 1. The probability that no head is observed is $\frac{1}{16}$ . 2. The probability that the experiment ends with three tosses is $\frac{1}{8}$ . Select the correct answer using the code given below:
1. A.1 only
2. B.2 only
3. C.Both 1 and 2
4. D.Neither 1 nor 2
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Answer: C
Q1122015 · 27 Sept 2015
If $x \in [0, 5]$ , then what is the probability that $x^{2} - 3 x + 2 \geq 0$ ?
1. A. $\frac{4}{5}$
2. B. $\frac{1}{5}$
3. C. $\frac{2}{5}$
4. D. $\frac{3}{5}$
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Answer: A
Q1132015 · 27 Sept 2015
A bag contains 4 white and 2 black balls and another bag contains 3 white and 5 black balls. If one ball is drawn from each bag, then the probability that one ball is white and one ball is black is
1. A. $\frac{5}{24}$
2. B. $\frac{13}{24}$
3. C. $\frac{1}{4}$
4. D. $\frac{2}{3}$
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Answer: B
Q1142015 · 27 Sept 2015
A problem in statistics is given to three students $A, B$ and $C$ whose chances of solving it independently are $\frac{1}{2}$ , $\frac{1}{3}$ and $\frac{1}{4}$ respectively. The probability that the problem will be solved is
1. A. $\frac{1}{12}$
2. B. $\frac{11}{12}$
3. C. $\frac{1}{2}$
4. D. $\frac{3}{4}$
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Answer: D
Q1152015 · 27 Sept 2015
An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probabilities of an accident involving a scooter driver, car driver and a truck driver are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. The probability that the person is a scooter driver is
1. A. $\frac{1}{52}$
2. B. $\frac{3}{52}$
3. C. $\frac{15}{52}$
4. D. $\frac{19}{52}$
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Answer: A
Q1162015 · 27 Sept 2015
A coin is tossed 5 times. The probability that tail appears an odd number of times, is
1. A. $\frac{1}{2}$
2. B. $\frac{1}{3}$
3. C. $\frac{2}{5}$
4. D. $\frac{1}{5}$
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Answer: A
Q1172015 · 27 Sept 2015
What is the probability that the sum of any two different single digit natural numbers is a prime number?
1. A. $\frac{5}{27}$
2. B. $\frac{7}{18}$
3. C. $\frac{1}{3}$
4. D.None of the above
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Answer: B
Q1182015 · 27 Sept 2015
What is $(1000000001)_{2} - (0.0101)_{2}$ equal to?
1. A. $(512.6775)_{10}$
2. B. $(512.6875)_{10}$
3. C. $(512.6975)_{10}$
4. D. $(512.0909)_{10}$
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Answer: B
Q1192015 · 27 Sept 2015
For the next two (02) items that follow: Consider $f^{'} (x) = \frac{x ^{2}}{2} - k x + 1$ such that $f (0) = 0 and f (3) = 15$ The value of $k$ is
1. A. $\frac{5}{3}$
2. B. $\frac{3}{5}$
3. C. $- \frac{5}{3}$
4. D. $- \frac{3}{5}$
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Answer: C
Q1202015 · 27 Sept 2015
For the next two (02) items that follow: Consider $f^{'} (x) = \frac{x ^{2}}{2} - k x + 1$ such that $f (0) = 0 and f (3) = 15$ $f^{''} (- \frac{2}{3})$ is equal to
1. A. $- 1$
2. B. $\frac{1}{3}$
3. C. $\frac{1}{2}$
4. D.1
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Answer: D
Q1082015 · 19 Apr 2015
Two men hit at a target with probabilities 1/2 and 1/3 respectively. What is the probability that exactly one of them hits the target?
1. A.1/2
2. B.1/3
3. C.1/6
4. D.2/3
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Answer: A
Q1092015 · 19 Apr 2015
Two similar boxes $B_{i}$ ( $i = 1, 2$ ) contain $(i + 1)$ red and $(5 - i - 1)$ black balls. One box is chosen at random and two balls are drawn randomly. What is the probability that both the balls are of different colours?
1. A.1/2
2. B.3/10
3. C.2/5
4. D.3/5
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Answer: D
Q1102015 · 19 Apr 2015
In an examination, the probability of a candidate solving a question is 1/2. Out of given 5 questions in the examination, what is the probability that the candidate was able to solve at least 2 questions?
1. A.1/64
2. B.3/16
3. C.1/2
4. D.13/16
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Answer: D
Q1112015 · 19 Apr 2015
If $A \subseteq B$ , then which one of the following is not correct?
1. A. $P (A \cap \overline{B}) = 0$
2. B. $P (A ∣ B) = \frac{P ( A )}{P ( B )}$
3. C. $P (B ∣ A) = \frac{P ( B )}{P ( A )}$
4. D. $P (A ∣ (A \cup B)) = \frac{P ( A )}{P ( B )}$
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Answer: C
Q1122015 · 19 Apr 2015
The mean and the variance in a binomial distribution are found to be 2 and 1 respectively. The probability $P (X = 0)$ is
1. A.1/2
2. B.1/4
3. C.1/8
4. D.1/16
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Answer: D
Q1132015 · 19 Apr 2015
If $A$ and $B$ are two events such that $P (A \cup B) = \frac{3}{4}$ , $P (A \cap B) = \frac{1}{4}$ and $P (\overline{A}) = \frac{2}{3}$ , then what is $P (B)$ equal to?
1. A.1/3
2. B.2/3
3. C.1/8
4. D.2/9
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Answer: B
Q1142015 · 19 Apr 2015
In throwing of two dice, the number of exhaustive events that ‘5’ will never appear on any one of the dice is
1. A.5
2. B.18
3. C.25
4. D.36
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Answer: C
Q1152015 · 19 Apr 2015
Two cards are drawn successively without replacement from a well-shuffled pack of 52 cards. The probability of drawing two aces is
1. A.1/26
2. B.1/221
3. C.4/223
4. D.1/13
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Answer: B