Probability · JEE Main previous year questions

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2026 16 questions

Q62026 · 8 Apr 2026 · Shift 2
A candidate has to go to the examination centre to appear in an examination. The candidate uses only one means of transportation for the entire distance out of bus, scooter and car. The probabilities of the candidate going by bus, scooter and car, respectively, are $\frac{2}{5}$ , $\frac{1}{5}$ and $\frac{2}{5}$ . The probabilities that the candidate reaches late at the examination centre are $\frac{1}{5}$ , $\frac{1}{3}$ and $\frac{1}{4}$ if the candidate uses bus, scooter and car, respectively. Given that the candidate reached late at the examination centre, the probability that the candidate travelled by bus is :
1. A. $\frac{11}{37}$
2. B. $\frac{12}{37}$
3. C. $\frac{13}{37}$
4. D. $\frac{14}{37}$
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Answer: B
Q102026 · 6 Apr 2026 · Shift 1
A bag contains $(N + 1)$ coins $-$ N fair coins, and one coin with 'Head' on both sides. A coin is selected at random and tossed. If the probability of getting 'Head' is $\frac{9}{16}$ , then N is equal to:
1. A.5
2. B.7
3. C.8
4. D.9
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Answer: B
Q92026 · 6 Apr 2026 · Shift 2
A bag contains 6 blue and 6 green balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each drawn pair consists of one blue and one green ball is :
1. A. $\frac{63}{925}$
2. B. $\frac{17}{231}$
3. C. $\frac{16}{231}$
4. D. $\frac{64}{925}$
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Answer: C
Q72026 · 5 Apr 2026 · Shift 1
A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the envelope just two consecutive letters AN are visible. The probability, that the letter came from ANANTPUR, is:
1. A. $\frac{7}{10}$
2. B. $\frac{10}{17}$
3. C. $\frac{12}{19}$
4. D. $\frac{7}{19}$
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Answer: B
Q82026 · 5 Apr 2026 · Shift 2
The probabilities that players A and B of a team are selected for the captaincy for a tournament are $0.6$ and $0.4$ , respectively. If A is selected the captain, the probability that the team wins the tournament is $0.8$ and if B is selected the captain, the probability that the team wins the tournament is $0.7$ . Then the probability, that the team wins the tournament, is :
1. A. $0.74$
2. B. $0.76$
3. C. $0.72$
4. D. $0.78$
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Answer: B
Q212026 · 4 Apr 2026 · Shift 1· Numerical answer
A coin is tossed 8 times. If the probability that exactly 4 heads appear in the first six tosses and exactly 3 heads appear in the last five tosses is $p$ , then $96 p$ is equal to _________.
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Answer: 9
Q212026 · 4 Apr 2026 · Shift 2· Numerical answer
From a month of 31 days, 3 different dates are selected at random. If the probability that these dates are in an increasing A.P. is equal to $\frac{a}{b}$ , where $a, b \in N$ and $g cd (a, b) = 1$ , then $a + b$ is equal to ____.
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Answer: 944
Q232026 · 2 Apr 2026 · Shift 1· Numerical answer
One mole of an alkane (x) requires 8 mole oxygen for complete combustion. Sum of number of carbon and hydrogen atoms in the alkane (x) is ________.
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Answer: 81
Q82026 · 2 Apr 2026 · Shift 2
A man throws a fair coin repeatedly. He gets 10 points for each head he throws and 5 points for each tail he throws. If the probability that he gets exactly 30 points is $\frac{m}{n}$ , $g cd (m, n) = 1$ , then $m + n$ is equal to :
1. A.53
2. B.55
3. C.107
4. D.105
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Answer: C
Q32026 · 28 Jan 2026 · Shift 1
A bag contains $10$ balls out of which $k$ are red and $(10 - k)$ are black, where $0 \leq k \leq 10$ . If three balls are drawn at random without replacement and all of them are found to be black, then the probability that the bag contains $1$ red and $9$ black balls is:
1. A. $\frac{7}{110}$
2. B. $\frac{7}{11}$
3. C. $\frac{7}{55}$
4. D. $\frac{14}{55}$
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Answer: D
Q172026 · 28 Jan 2026 · Shift 2
The probability distribution of a random variable X is given below : $X P(X) 4 k \frac{2}{15} \frac{30}{7} k \frac{1}{15} \frac{32}{7} k \frac{2}{15} \frac{34}{7} k \frac{1}{5} \frac{36}{7} k \frac{1}{15} \frac{38}{7} k \frac{2}{15} \frac{40}{7} k \frac{1}{5} 6 k \frac{1}{15}$ If $E(X) = \frac{263}{15}$ , then $P(X < 20)$ is equal to :
1. A. $\frac{3}{5}$
2. B. $\frac{14}{15}$
3. C. $\frac{8}{15}$
4. D. $\frac{11}{15}$
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Answer: D
Q122026 · 24 Jan 2026 · Shift 1
From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one by one with replacement. Then the probability of getting at least 7 defective bulbs is
1. A. $\frac{73}{1 0 ^{8}}$
2. B. $\frac{67}{1 0 ^{8}}$
3. C. $\frac{7}{1 0 ^{7}}$
4. D. $\frac{81}{1 0 ^{8}}$
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Answer: A
Q242026 · 23 Jan 2026 · Shift 1· Numerical answer
From the first 100 natural numbers, two numbers first $a$ and then $b$ are selected randomly without replacement. If the probability that $a - b ⩾ 10$ is $\frac{m}{n}$ , $g cd (m, n) = 1$ , then $m + n$ is equal to ____ .
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Answer: 311
Q72026 · 23 Jan 2026 · Shift 2
Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is randomly picked up from the bag B and mixed up with the balls in the bag A . Then a ball is randomly drawn from the bag A . If the probability, that the ball drawn is white, is $\frac{p}{q}$ , $gcd (p, q) = 1$ , then $p + q$ is equal to
1. A.24
2. B.22
3. C.23
4. D.21
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Answer: C
Q12026 · 22 Jan 2026 · Shift 1
Two distinct numbers $a$ and $b$ are selected at random from $1, 2, 3, \dots, 50$ . The probability, that their product $ab$ is divisible by 3 , is
1. A. $\frac{272}{1225}$
2. B. $\frac{561}{1225}$
3. C. $\frac{664}{1225}$
4. D. $\frac{8}{25}$
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Answer: C
Q152026 · 22 Jan 2026 · Shift 1
If a random variable $x$ has the probability distribution $x P (x) 00 1 2 k 2 k 3 3 k 4 2 k^{2} 5 2 k 6 k^{2} + k 7 7 k^{2}$ then $P (3 < x \leq 6)$ is equal to
1. A.0.34
2. B.0.64
3. C.0.22
4. D.0.33
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Answer: D