Probability · JEE Main previous year questions

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2025 12 questions

Q172025 · 8 Apr 2025 · Shift 2
If $A$ and $B$ are two events such that $P (A) = 0.7$ , $P (B) = 0.4$ and $P (A \cap \overline{B}) = 0.5$ , where $\overline{B}$ denotes the complement of $B$ , then $P (B ∣ (A \cup \overline{B}))$ is equal to
1. A. $\frac{1}{3}$
2. B. $\frac{1}{2}$
3. C. $\frac{1}{4}$
4. D. $\frac{1}{6}$
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Answer: C
Q112025 · 4 Apr 2025 · Shift 1
The probability, of forming a 12 persons committee from 4 engineers, 2 doctors and 10 professors containing at least 3 engineers and at least 1 doctor, is
1. A. $\frac{129}{182}$
2. B. $\frac{17}{26}$
3. C. $\frac{19}{26}$
4. D. $\frac{103}{182}$
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Answer: A
Q222025 · 4 Apr 2025 · Shift 2· Numerical answer
A card from a pack of 52 cards is lost. From the remaining 51 cards, n cards are drawn and are found to be spades. If the probability of the lost card to be a spade is $\frac{11}{50}$ , then n is equal to ____ .
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Answer: 2
Q212025 · 3 Apr 2025 · Shift 1· Numerical answer
All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the word at serial number $n$ be denoted by $W_{n}$ . Let the probability $P (W_{n})$ of choosing the word $W_{n}$ satisfy $P (W_{n}) = 2 P (W_{n - 1}), n > 1$ . If $P (CDBEA) = \frac{2 ^{α}}{2 ^{β} - 1}$ , $α, β \in N$ , then $α + β$ is equal to : ____
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Answer: 183
Q152025 · 3 Apr 2025 · Shift 2
If the probability that the random variable $X$ takes the value $x$ is given by $P (X = x) = k (x + 1) 3^{- x}, x = 0, 1, 2, 3 \dots$ , where $k$ is a constant, then $P (X \geq 3)$ is equal to
1. A. $\frac{1}{9}$
2. B. $\frac{8}{27}$
3. C. $\frac{7}{27}$
4. D. $\frac{4}{9}$
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Answer: A
Q212025 · 2 Apr 2025 · Shift 1· Numerical answer
Three distinct numbers are selected randomly from the set ${1, 2, 3, \dots, 40}$ . If the probability, that the selected numbers are in an increasing G.P., is $\frac{m}{n}$ , $g cd (m, n) = 1$ , then $m + n$ is equal to _________ .
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Answer: 2477
Q202025 · 2 Apr 2025 · Shift 2
Given three identical bags each containing 10 balls, whose colours are as follows : $Bag I Bag II Bag III Red 345 Blue 231 Green 534$ A person chooses a bag at random and takes out a ball. If the ball is Red, the probability that it is from bag I is p and if the ball is Green, the probability that it is from bag III is $q$ , then the value of $(\frac{1}{p} + \frac{1}{q})$ is:
1. A.6
2. B.9
3. C.7
4. D.8
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Answer: C
Q92025 · 29 Jan 2025 · Shift 2
Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains $n$ white balls and 3 black balls. One ball is drawn randomly from Bag 1 and transferred to Bag 2. A ball is then drawn randomly from Bag 2. If the probability, that the ball drawn is white, is $\frac{29}{45}$ , then $n$ is equal to:
1. A. $5$
2. B. $6$
3. C. $4$
4. D. $3$
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Answer: B
Q102025 · 28 Jan 2025 · Shift 1
Two number $k_{1}$ and $k_{2}$ are randomly chosen from the set of natural numbers. Then, the probability that the value of $i^{k_{1}} + i^{k_{2}}$ , ( $i = - 1$ ) is non-zero, equals
1. A. $\frac{3}{4}$
2. B. $\frac{1}{2}$
3. C. $\frac{1}{4}$
4. D. $\frac{2}{3}$
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Answer: A
Q122025 · 24 Jan 2025 · Shift 1
$A$ and $B$ alternately throw a pair of dice. A wins if he throws a sum of $5$ before $B$ throws a sum of $8$ , and $B$ wins if he throws a sum of $8$ before $A$ throws a sum of $5$ . The probability, that A wins if A makes the first throw, is
1. A. $\frac{8}{19}$
2. B. $\frac{9}{19}$
3. C. $\frac{8}{17}$
4. D. $\frac{9}{17}$
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Answer: B
Q52025 · 23 Jan 2025 · Shift 2
1. A. $\frac{3}{5}$
2. B. $\frac{4}{5}$
3. C. $\frac{23}{30}$
4. D. $\frac{7}{10}$
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Answer: B
Q132025 · 22 Jan 2025 · Shift 1
Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the probability that the first selected ball is black, given that the second selected ball is also black, is $\frac{m}{n}$ , where $g cd (m, n) = 1$ , then $m + n$ is equal to :
1. A.4
2. B.14
3. C.11
4. D.13
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Answer: B