PROBABILITY - Pyqs

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Q1
Two dice are thrown. Find the probability that the sum is 8.
(Exam: IIT-JEE Year: 1998)
(A) 5/36
(B) 1/6
(C) 4/36
(D) 1/9
Q2
A card is drawn from a standard deck. Find \(P(\text{Ace}|\text{Red})\).
(Exam: AIPMT Year: 2006)
(A) 1/13
(B) 2/13
(C) 1/26
(D) 1/52
Q3
Three coins are tossed. Probability of exactly two heads is
(Exam: BITSAT Year: 2012)
(A) 1/2
(B) 3/8
(C) 1/8
(D) 3/4
Q4
If \(P(A)=0.6,P(B)=0.5,P(A\cap B)=0.3\), find \(P(A|B)\).
(Exam: JEE Main Year: 2015)
(A) 0.5
(B) 0.6
(C) 0.3
(D) 0.4
Q5
Two cards are drawn without replacement. Probability both are kings is
(Exam: AIIMS Year: 2009)
(A) 1/221
(B) 2/221
(C) 4/221
(D) 6/221
Q6
If events \(A,B\) are independent, then
(Exam: KVPY Year: 2014)
(A) \(P(A+B)=P(A)P(B)\)
(B) \(P(A|B)=P(A)\)
(C) \(P(A)=P(B)\)
(D) \(A=B\)
Q7
A die is thrown. Probability of getting a prime number is
(Exam: Olympiad Year: 2010)
(A) 1/2
(B) 1/3
(C) 2/3
(D) 5/6
Q8
From numbers 1–10 one is chosen randomly. Probability of multiple of 3 is
(Exam: JEE Main Year: 2016)
(A) 1/5
(B) 2/5
(C) 3/10
(D) 1/3
Q9
Probability that a leap year has 53 Sundays is
(Exam: IIT-JEE Year: 2002)
(A) 1/7
(B) 2/7
(C) 3/7
(D) 4/7
Q10
Find \(P(A\cup B)\) if \(P(A)=0.4,P(B)=0.5,P(A\cap B)=0.2\).
(Exam: NEET Year: 2018)
(A) 0.7
(B) 0.6
(C) 0.5
(D) 0.9
Q11
Two coins are tossed. Probability of getting at least one head is
(Exam: JEE Main Year: 2014)
(A) 1/4
(B) 1/2
(C) 3/4
(D) 2/3
Q12
A bag contains 5 red and 3 blue balls. Two balls are drawn without replacement. Probability both are red is
(Exam: NEET Year: 2019)
(A) 5/14
(B) 10/21
(C) 25/56
(D) 3/8
Q13
Find \(P(A\cap B)\) if \(P(A)=0.5,P(B)=0.4\) and \(A,B\) are independent.
(Exam: BITSAT Year: 2016)
(A) 0.1
(B) 0.2
(C) 0.3
(D) 0.4
Q14
Three dice are thrown. Probability that their sum is 9 is
(Exam: IIT-JEE Year: 2001)
(A) 25/216
(B) 20/216
(C) 30/216
(D) 15/216
Q15
A card is drawn. Given that it is black, find the probability it is a face card.
(Exam: AIIMS Year: 2010)
(A) 3/13
(B) 6/13
(C) 1/13
(D) 3/26
Q16
If \(P(A|B)=P(A)\), then events \(A,B\) are
(Exam: KVPY Year: 2013)
(A) mutually exclusive
(B) equally likely
(C) independent
(D) complementary
Q17
A fair coin is tossed 4 times. Probability of exactly two heads is
(Exam: Olympiad Year: 2012)
(A) 1/8
(B) 3/8
(C) 1/2
(D) 1/4
Q18
If \(P(A)=0.35\), find \(P(A')\).
(Exam: JEE Main Year: 2017)
(A) 0.35
(B) 0.65
(C) 0.5
(D) 0.75
Q19
Mean of a random variable taking values \(1,2,3,4,5,6\) each with equal probability is
(Exam: NEET Year: 2020)
(A) 3
(B) 3.5
(C) 4
(D) 2.5
Q20
Two cards are drawn. Probability that at least one is an ace is
(Exam: IIT-JEE Year: 2004)
(A) 33/221
(B) 1/13
(C) 4/51
(D) 17/221
Q21
Probability of getting exactly one success in two Bernoulli trials with \(p=\frac13\) is
(Exam: BITSAT Year: 2015)
(A) 2/9
(B) 4/9
(C) 1/3
(D) 5/9
Q22
Expected number of tosses to get first head is
(Exam: Olympiad Year: 2014)
(A) 1
(B) 2
(C) 3
(D) 4
Q23
Variance of binomial distribution is
(Exam: JEE Advanced Year: 2018)
(A) \(np\)
(B) \(nq\)
(C) \(npq\)
(D) \(p/q\)
Q24
A die is thrown twice. Probability of at least one six is
(Exam: NEET Year: 2016)
(A) 1/6
(B) 11/36
(C) 5/36
(D) 1/3
Q25
Probability that both drawn cards are aces is
(Exam: IIT-JEE Year: 1999)
(A) 1/221
(B) 2/221
(C) 4/221
(D) 6/221
Q26
From digits 1–9 one is chosen randomly. Probability of even digit is
(Exam: JEE Main Year: 2019)
(A) 4/9
(B) 5/9
(C) 1/2
(D) 3/9
Q27
Two dice are thrown. Probability that product is even is
(Exam: Olympiad Year: 2011)
(A) 1/2
(B) 3/4
(C) 2/3
(D) 5/6
Q28
Find \(P(A|B)\) if \(P(A\cap B)=0.12\) and \(P(B)=0.3\).
(Exam: AIIMS Year: 2012)
(A) 0.2
(B) 0.3
(C) 0.4
(D) 0.5
Q29
Probability that a randomly chosen integer from 1 to 100 is divisible by 5 is
(Exam: JEE Main Year: 2018)
(A) 1/10
(B) 1/5
(C) 2/5
(D) 1/4
Q30
A leap year has 53 Sundays with probability
(Exam: IIT-JEE Year: 2003)
(A) 1/7
(B) 2/7
(C) 3/7
(D) 4/7
Q31
Three cards are drawn at random. Probability that all belong to the same suit is
(Exam: JEE Advanced Year: 2016)
(A) \(\frac{4C(13,3)}{C(52,3)}\)
(B) \(\frac{C(13,3)}{C(52,3)}\)
(C) \(\frac14\)
(D) \(\frac3{13}\)
Q32
Probability of at least one tail when three coins are tossed is
(Exam: NEET Year: 2017)
(A) 1/8
(B) 3/8
(C) 7/8
(D) 1/2
Q33
Two dice are thrown. Probability that the sum is prime is
(Exam: Olympiad Year: 2015)
(A) 5/12
(B) 1/3
(C) 15/36
(D) 7/36
Q34
Expected value of outcomes of a fair die is
(Exam: BITSAT Year: 2014)
(A) 3
(B) 3.5
(C) 4
(D) 2.5
Q35
Probability that no digit repeats in a random 3-digit number is
(Exam: JEE Main Year: 2020)
(A) 72/100
(B) 81/100
(C) 9/10
(D) 8/9
Q36
Using Bayes theorem, posterior probability is obtained by
(Exam: KVPY Year: 2018)
(A) addition
(B) multiplication
(C) normalization
(D) differentiation
Q37
A card drawn is not a face card. Probability equals
(Exam: NEET Year: 2015)
(A) 12/52
(B) 40/52
(C) 3/13
(D) 10/13
Q38
Mean of binomial distribution is
(Exam: JEE Advanced Year: 2019)
(A) \(np\)
(B) \(nq\)
(C) \(pq\)
(D) \(n/p\)
Q39
Probability that exactly one six appears in two throws of a die is
(Exam: Olympiad Year: 2013)
(A) 5/18
(B) 1/6
(C) 10/36
(D) 2/9
Q40
Law of total probability applies when
(Exam: IIT-JEE Year: 2000)
(A) events are independent
(B) sample space is infinite
(C) events form a partition
(D) outcomes equally likely
Q41
A box contains 3 defective and 7 good items. One item is selected at random. Find the probability that it is defective.
(Exam: JEE Main Year: 2016)
(A) 3/7
(B) 3/10
(C) 7/10
(D) 1/3
Q42
Two balls are drawn successively with replacement from a bag containing 4 red and 6 blue balls. Probability that both are blue is
(Exam: NEET Year: 2018)
(A) 9/25
(B) 16/25
(C) 36/100
(D) 3/10
Q43
If \(P(A)=0.7\) and \(P(B)=0.6\), find the maximum possible value of \(P(A\cap B)\).
(Exam: Olympiad Year: 2017)
(A) 0.3
(B) 0.6
(C) 0.7
(D) 0.9
Q44
A fair die is thrown. Find the probability that the number obtained is neither prime nor composite.
(Exam: AIIMS Year: 2011)
(A) 1/6
(B) 1/3
(C) 1/2
(D) 2/3
Q45
Two cards are drawn at random. Find the probability that one is a heart and the other is a spade.
(Exam: IIT-JEE Year: 2005)
(A) 13/102
(B) 26/221
(C) 52/221
(D) 1/4
Q46
A coin is tossed until a tail appears. Find the probability that the tail appears on the third toss.
(Exam: KVPY Year: 2015)
(A) 1/4
(B) 1/8
(C) 3/8
(D) 1/2
Q47
Find the probability that exactly two heads occur when three fair coins are tossed.
(Exam: JEE Main Year: 2019)
(A) 1/4
(B) 3/8
(C) 1/2
(D) 5/8
Q48
If two events are mutually exclusive with probabilities 0.3 and 0.4, then \(P(A\cup B)\) is
(Exam: NEET Year: 2017)
(A) 0.12
(B) 0.7
(C) 0.5
(D) 0.1
Q49
A number is chosen at random from 1 to 20. Find probability that it is divisible by 4 or 5.
(Exam: Olympiad Year: 2016)
(A) 2/5
(B) 9/20
(C) 1/2
(D) 7/20
Q50
Using Bayes theorem, a student solves a problem correctly with probability 0.6. If he solves it correctly, probability it was easy is 0.7. Find probability that the problem was easy and solved correctly.
(Exam: JEE Advanced Year: 2018)
(A) 0.42
(B) 0.6
(C) 0.7
(D) 0.3

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