Probability · JEE Main previous year questions

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2020 13 questions

Q92020 · 6 Sept 2020 · Shift 1
Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference, is :
1. A. $\frac{10}{99}$
2. B. $\frac{5}{33}$
3. C. $\frac{15}{101}$
4. D. $\frac{5}{101}$
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Answer: B
Q12020 · 6 Sept 2020 · Shift 2
The probabilities of three events A, B and C are given by $P (A) = 0.6$ , $P (B) = 0.4$ and $P (C) = 0.5$ . If $P (A \cup B) = 0.8$ , $P (A \cap C) = 0.3$ , $P (A \cap B \cap C) = 0.2$ , $P (B \cap C) = β$ and $P (A \cup B \cup C) = α$ , where $0.85 \leq α \leq 0.95$ , then $β$ lies in the interval :
1. A. $[0.35, 0.36]$
2. B. $[0.20, 0.25]$
3. C. $[0.25, 0.35]$
4. D. $[0.36, 0.40]$
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Answer: C
Q12020 · 3 Sept 2020 · Shift 1
A dice is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of 4. Then the conditional probability that the score 4 has appeared atleast once is :
1. A. $\frac{1}{8}$
2. B. $\frac{1}{9}$
3. C. $\frac{1}{4}$
4. D. $\frac{1}{3}$
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Answer: B
Q162020 · 3 Sept 2020 · Shift 2
The probability that a randomly chosen 5-digit number is made from exactly two digits is :
1. A. $\frac{150}{1 0 ^{4}}$
2. B. $\frac{134}{1 0 ^{4}}$
3. C. $\frac{121}{1 0 ^{4}}$
4. D. $\frac{135}{1 0 ^{4}}$
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Answer: D
Q32020 · 2 Sept 2020 · Shift 1
Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. A box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was drawn from Box I is :
1. A. $\frac{8}{17}$
2. B. $\frac{2}{3}$
3. C. $\frac{2}{5}$
4. D. $\frac{4}{17}$
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Answer: A
Q112020 · 2 Sept 2020 · Shift 2
Let $E^{C}$ denote the complement of an event $E$ . Let $E_{1}, E_{2}$ and $E_{3}$ be any pairwise independent events with $P (E_{1}) > 0$ and $P (E_{1} \cap E_{2} \cap E_{3}) = 0$ . Then $P (E_{2}^{C} \cap E_{3}^{C} / E_{1})$ is equal to :
1. A. $P (E_{3}^{C}) - P (E_{2})$
2. B. $P (E_{2}^{C}) + P (E_{3})$
3. C. $P (E_{3}^{C}) - P (E_{2}^{C})$
4. D. $P (E_{3}) - P (E_{2}^{C})$
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Answer: A
Q42020 · 9 Jan 2020 · Shift 1
In a box, there are 20 cards, out of which 10 are labelled as A and the remaining 10 are labelled as B. Cards are drawn at random, one after the other and with replacement, till a second A-card is obtained. The probability that the second A-card appears before the third B-card is :
1. A. $\frac{13}{16}$
2. B. $\frac{11}{16}$
3. C. $\frac{15}{16}$
4. D. $\frac{9}{16}$
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Answer: B
Q62020 · 9 Jan 2020 · Shift 2
A random variable X has the following probability distribution : $X : P (X) : 1 K^{2} 2 2 K 3 K 4 2 K 5 5 K^{2}$ Then $P (X > 2)$ is equal to :
1. A. $\frac{1}{6}$
2. B. $\frac{7}{12}$
3. C. $\frac{1}{36}$
4. D. $\frac{23}{36}$
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Answer: D
Q92020 · 9 Jan 2020 · Shift 2
If 10 different balls are to be placed in 4 distinct boxes at random, then the probability that two of these boxes contain exactly 2 and 3 balls is :
1. A. $\frac{965}{2 ^{11}}$
2. B. $\frac{965}{2 ^{10}}$
3. C. $\frac{945}{2 ^{11}}$
4. D. $\frac{945}{2 ^{10}}$
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Answer: D
Q122020 · 8 Jan 2020 · Shift 1
Let A and B be two independent events such that $P (A) = \frac{1}{3}$ and $P (B) = \frac{1}{6}$ . Then, which of the following is TRUE?
1. A. $P (\frac{A}{A \cup B}) = \frac{1}{4}$
2. B. $P (\frac{A}{B}) = \frac{2}{3}$
3. C. $P (\frac{A ^{'}}{B ^{'}}) = \frac{1}{3}$
4. D. $P (\frac{A}{B ^{'}}) = \frac{1}{3}$
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Answer: D
Q122020 · 8 Jan 2020 · Shift 2
Let A and B be two events such that the probability that exactly one of them occurs is $\frac{2}{5}$ and the probability that A or B occurs is $\frac{1}{2}$ , then the probability of both of them occur together is :
1. A.0.20
2. B.0.02
3. C.0.01
4. D.0.10
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Answer: D
Q92020 · 7 Jan 2020 · Shift 1
An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value of k when k consecutive heads are obtained for $k = 3, 4, 5$ , otherwise X takes the value -1. Then the expected value of X, is :
1. A. $- \frac{3}{16}$
2. B. $- \frac{1}{8}$
3. C. $\frac{1}{8}$
4. D. $\frac{3}{16}$
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Answer: C
Q142020 · 7 Jan 2020 · Shift 2
In a workshop, there are five machines and the probability of any one of them to be out of service on a day is $\frac{1}{4}$ . If the probability that at most two machines will be out of service on the same day is $(\frac{3}{4})^{3} k$ , then $k$ is equal to :
1. A. $\frac{17}{4}$
2. B. $\frac{17}{2}$
3. C. $\frac{17}{8}$
4. D.4
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Answer: C