Probability · JEE Main previous year questions

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2021 15 questions

Q42021 · 1 Sept 2021 · Shift 2
1. A. $\frac{2}{7}$
2. B. $\frac{1}{18}$
3. C. $\frac{1}{7}$
4. D. $\frac{1}{9}$
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Answer: B
Q72021 · 26 Aug 2021 · Shift 2
A fair die is tossed until six is obtained on it. Let x be the number of required tosses, then the conditional probability $P (x \geq 5 ∣ x > 2)$ is :
1. A. $\frac{125}{216}$
2. B. $\frac{11}{36}$
3. C. $\frac{5}{6}$
4. D. $\frac{25}{36}$
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Answer: D
Q92021 · 26 Aug 2021 · Shift 2
Two fair dice are thrown. The numbers on them are taken as $λ$ and $μ$ , and a system of linear equations $x + y + z = 5$ $x + 2 y + 3 z = μ$ $x + 3 y + λ z = 1$ is constructed. If p is the probability that the system has a unique solution and q is the probability that the system has no solution, then :
1. A. $p = \frac{1}{6}$ and $q = \frac{1}{36}$
2. B. $p = \frac{5}{6}$ and $q = \frac{5}{36}$
3. C. $p = \frac{5}{6}$ and $q = \frac{1}{36}$
4. D. $p = \frac{1}{6}$ and $q = \frac{5}{36}$
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Answer: B
Q172021 · 27 Jul 2021 · Shift 2
A student appeared in an examination consisting of 8 true-false type questions. The student guesses the answers with equal probability. the smallest value of n, so that the probability of guessing at least 'n' correct answers is less than $\frac{1}{2}$ , is :
1. A.5
2. B.6
3. C.3
4. D.4
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Answer: A
Q122021 · 25 Jul 2021 · Shift 1
Let 9 distinct balls be distributed among 4 boxes, $B_{1}, B_{2}, B_{3}$ and $B_{4}$ . If the probability that $B_{3}$ contains exactly 3 balls is $k (\frac{3}{4})^{9}$ then k lies in the set :
1. A. ${x \in R : ∣ x - 3∣ < 1}$
2. B. ${x \in R : ∣ x - 2∣ \leq 1}$
3. C. ${x \in R : ∣ x - 1∣ < 1}$
4. D. ${x \in R : ∣ x - 5∣ \leq 1}$
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Answer: A
Q152021 · 25 Jul 2021 · Shift 2
Let X be a random variable such that the probability function of a distribution is given by $P (X = 0) = \frac{1}{2}, P (X = j) = \frac{1}{3 ^{j}} (j = 1, 2, 3, \dots, \infty)$ . Then the mean of the distribution and P(X is positive and even) respectively are :
1. A. $\frac{3}{8}$ and $\frac{1}{8}$
2. B. $\frac{3}{4}$ and $\frac{1}{8}$
3. C. $\frac{3}{4}$ and $\frac{1}{9}$
4. D. $\frac{3}{4}$ and $\frac{1}{16}$
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Answer: B
Q252021 · 25 Jul 2021 · Shift 2· Numerical answer
A fair coin is tossed n-times such that the probability of getting at least one head is at least 0.9. Then the minimum value of n is ______________.
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Answer: 4
Q142021 · 20 Jul 2021 · Shift 1
Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word is :
1. A. $\frac{1}{66}$
2. B. $\frac{1}{11}$
3. C. $\frac{1}{9}$
4. D. $\frac{2}{11}$
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Answer: B
Q152021 · 20 Jul 2021 · Shift 1
The probability of selecting integers $a \in [- 5, 30]$ such that $x^{2} + 2 (a + 4) x - 5 a + 64 > 0$ , for all $x \in R$ , is :
1. A. $\frac{7}{36}$
2. B. $\frac{2}{9}$
3. C. $\frac{1}{6}$
4. D. $\frac{1}{4}$
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Answer: B
Q162021 · 18 Mar 2021 · Shift 2
Let in a Binomial distribution, consisting of 5 independent trials, probabilities of exactly 1 and 2 successes be 0.4096 and 0.2048 respectively. Then the probability of getting exactly 3 successes is equal to :
1. A. $\frac{40}{243}$
2. B. $\frac{128}{625}$
3. C. $\frac{80}{243}$
4. D. $\frac{32}{625}$
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Answer: D
Q132021 · 16 Mar 2021 · Shift 1
A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is :
1. A. $\frac{39}{50}$
2. B. $\frac{3}{4}$
3. C. $\frac{22}{425}$
4. D. $\frac{52}{867}$
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Answer: A
Q172021 · 26 Feb 2021 · Shift 1
A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to probability of getting 9 heads, then the probability of getting 2 heads is :
1. A. $\frac{15}{2 ^{8}}$
2. B. $\frac{15}{2 ^{12}}$
3. C. $\frac{15}{2 ^{13}}$
4. D. $\frac{15}{2 ^{14}}$
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Answer: C
Q142021 · 26 Feb 2021 · Shift 2
A seven digit number is formed using digits 3, 3, 4, 4, 4, 5, 5. The probability, that number so formed is divisible by 2, is :
1. A. $\frac{1}{7}$
2. B. $\frac{4}{7}$
3. C. $\frac{6}{7}$
4. D. $\frac{3}{7}$
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Answer: D
Q52021 · 25 Feb 2021 · Shift 2
Let A be a set of all 4-digit natural numbers whose exactly one digit is 7. Then the probability that a randomly chosen element of A leaves remainder 2 when divided by 5 is :
1. A. $\frac{2}{9}$
2. B. $\frac{1}{5}$
3. C. $\frac{122}{297}$
4. D. $\frac{97}{297}$
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Answer: D
Q122021 · 25 Feb 2021 · Shift 2
In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140 are non-smokers and vegetarian. Their chances of getting a particular chest disorder are 35%, 20% and 10% respectively. A person is chosen from the group at random and is found to be suffering from the chest disorder. The probability that the selected person is a smoker and non-vegetarian is :
1. A. $\frac{14}{45}$
2. B. $\frac{8}{45}$
3. C. $\frac{7}{45}$
4. D. $\frac{28}{45}$
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Answer: D