1. Five cards are drawn at random one after another from a deck of 52 cards with replacement. The probability that, a spade card occurs at most once is
a) 81/128 b) 27/32 c) 37/64 d) 81/256
2. A bag contains 4 tickets marked AAB, ABA, BAA, BBB. One ticket is drawn at random from the bag. Let Ei(i=1,2,3) denote the event that ith letter on the ticket is B; then which of the following is false?
a) E1 and E3 are independent
b) E2 and E3 are independent
c) E1 and E2 are independent
d) None of these
3.Probability that a factor of 30 29 is a multiple of 30 24 is
a) 81/128 b) 27/32 c) 37/64 d) 81/256
2. A bag contains 4 tickets marked AAB, ABA, BAA, BBB. One ticket is drawn at random from the bag. Let Ei(i=1,2,3) denote the event that ith letter on the ticket is B; then which of the following is false?
a) E1 and E3 are independent
b) E2 and E3 are independent
c) E1 and E2 are independent
d) None of these
3.Probability that a factor of 30 29 is a multiple of 30 24 is
a)
1/125 b)
6/125 c) 9/125 d)12/125
4. A biased coin is tossed 16 times. If the probability of getting 8 heads is same as that of getting 9 heads, then the probability of getting a head in a single toss is
a) 9/17 b) 8/17 c) 7/17 d) 10/17
5. In 512 sets of rolls of a fair six-sided die, the expected number of sets(rounded off to the nearest integer) in which 12 prime numbers and 3 non-prime numbers occur is
a) 5 b) 4 c) 7 d) 9
6. From a bag containing 8 white and 6 red balls, Ramu selected balls at random at a time first and then Somu selected 3 balls at random at a time without replacing Ramu's balls. Probability that the balls selected by Ramu are all white and that of Somu are all red
a) 5/429 b) 5/143 c) 5/286 d) 7/286
7. Among the aspirants of PSU jobs in BHEL, NTPC and HPCL, of a reputed university, the probabilities of a student getting selected in both BHEL and NTPC, in both NTPC and HPCL, in both HPCL and BHEL and in all the three among BHEL, NTPC and HPCL are 0.4, 0.3, 0.5 and 0.2 respectively. The probability that a student, among these aspirants, getting selected in exactly two of the three PSUs is ---------------------------
8. Two friends decided to meet between 7:00 p.m. and 8:00 p.m. on a certain day at a certain venue. They agreed that whoever arrived first among them at the venue would wait for at most 20 minutes for the other person. Find the probability that they will not meet on that day
a) 4/9 b) 5/9 c) 5/19 d) 13/18
9. Let S = { 0, 1,2,3,............2015}. If a number is selected at random from the set S, the probability that it is a prime factor of 2015 is
a) 3/2015 b) 1/1008 c) 1/226 d) 1/672
10. The probability that Rohan will pass atleast one of the two subjects Maths and Science is 0.6 and the probability that Rohan will pass both Maths and Science is 0.2. Then the sum of the probabilities of Rohan not passing Maths and not passing Science is
a) 0.4 b) 0.8 c) 1.2 d) 1.4
11. Two biased dice are thrown together. On one of them, 6 appears twice as often as any other number while on the other, an odd number appears thrice as frequently as an even number. What is the probability that the sum of the scores on them is 11 0r 12?
a) 1/12 b) 9/28 c) 3/28 d) 5/12
12. For two rolls of a fair die, the probability of getting a prime number in the first roll and a composite number in the second roll is ---------------------
13. Find the probability of a randomly selected leap year having 53 Mondays and 53 Wednesdays.
a) 1/7 b) 2/7 c) 3/7 d) 0
14. Urn 1 contains 14 marbles out of which 4 are blue. Urn 2 contains 16 marbles out of which 6 are blue. If one marble is drawn at random from each Urn simultaneously, the probability of getting exactly one marble is --------------
15. A man speaks truth 2 out of 3 times. He threw a biased coin, that has 60% chance of getting heads and reports that it turned up heads. What is the percentage of chance that it actually turned up on heads?
a) 25% b) 60% c) 66% d) 75%
16. At a certain factory, three machines M1, M2 and M3 manufacture 50%, 30% and 20% respectively, of the total spare parts. Out of this total, 4% of the output of M1, 2% of that of M2 and 5% of that of M3 end up being defective. If a randomly drawn spare part from the total output is defective, find the probability that the part was manufactured by either M1 or M3.
a) 4/5 b) 5/6 c) 11/12 d)1/6
17. An event is called statistically independent if
a) The probability of occurrence of one event is not affected by the occurrence of the other event.
b) The probability of occurrence of one event is affected by the occurrence of the other event.
c) The probability of occurrence of one event is affected by the occurrence of same event.
d) Non of these
Ans: Option a)
18. A fair coin is tossed 4 times, the probability that at least once head turns up is
a) 1/16
b) 15/16
c) 7/8
d) 1/8
19. The probability that Anil speaks truth is 4/5 while that of Bindu is 3/4, the probability that they are likely to contradict each other in stating the same fact is
a) 3/20
b) 4/5
c) 7/20
d) 1/5
23. For a biased coin, when tossed 12 times, probability of getting exactly 7 heads is same as probability of getting exactly 6 heads. Then the probability of getting heads, when that coin is tossed once is --------------------
a) 9/17 b) 8/17 c) 7/17 d) 10/17
5. In 512 sets of rolls of a fair six-sided die, the expected number of sets(rounded off to the nearest integer) in which 12 prime numbers and 3 non-prime numbers occur is
a) 5 b) 4 c) 7 d) 9
6. From a bag containing 8 white and 6 red balls, Ramu selected balls at random at a time first and then Somu selected 3 balls at random at a time without replacing Ramu's balls. Probability that the balls selected by Ramu are all white and that of Somu are all red
a) 5/429 b) 5/143 c) 5/286 d) 7/286
7. Among the aspirants of PSU jobs in BHEL, NTPC and HPCL, of a reputed university, the probabilities of a student getting selected in both BHEL and NTPC, in both NTPC and HPCL, in both HPCL and BHEL and in all the three among BHEL, NTPC and HPCL are 0.4, 0.3, 0.5 and 0.2 respectively. The probability that a student, among these aspirants, getting selected in exactly two of the three PSUs is ---------------------------
8. Two friends decided to meet between 7:00 p.m. and 8:00 p.m. on a certain day at a certain venue. They agreed that whoever arrived first among them at the venue would wait for at most 20 minutes for the other person. Find the probability that they will not meet on that day
a) 4/9 b) 5/9 c) 5/19 d) 13/18
9. Let S = { 0, 1,2,3,............2015}. If a number is selected at random from the set S, the probability that it is a prime factor of 2015 is
a) 3/2015 b) 1/1008 c) 1/226 d) 1/672
10. The probability that Rohan will pass atleast one of the two subjects Maths and Science is 0.6 and the probability that Rohan will pass both Maths and Science is 0.2. Then the sum of the probabilities of Rohan not passing Maths and not passing Science is
a) 0.4 b) 0.8 c) 1.2 d) 1.4
11. Two biased dice are thrown together. On one of them, 6 appears twice as often as any other number while on the other, an odd number appears thrice as frequently as an even number. What is the probability that the sum of the scores on them is 11 0r 12?
a) 1/12 b) 9/28 c) 3/28 d) 5/12
12. For two rolls of a fair die, the probability of getting a prime number in the first roll and a composite number in the second roll is ---------------------
13. Find the probability of a randomly selected leap year having 53 Mondays and 53 Wednesdays.
a) 1/7 b) 2/7 c) 3/7 d) 0
14. Urn 1 contains 14 marbles out of which 4 are blue. Urn 2 contains 16 marbles out of which 6 are blue. If one marble is drawn at random from each Urn simultaneously, the probability of getting exactly one marble is --------------
15. A man speaks truth 2 out of 3 times. He threw a biased coin, that has 60% chance of getting heads and reports that it turned up heads. What is the percentage of chance that it actually turned up on heads?
a) 25% b) 60% c) 66% d) 75%
16. At a certain factory, three machines M1, M2 and M3 manufacture 50%, 30% and 20% respectively, of the total spare parts. Out of this total, 4% of the output of M1, 2% of that of M2 and 5% of that of M3 end up being defective. If a randomly drawn spare part from the total output is defective, find the probability that the part was manufactured by either M1 or M3.
a) 4/5 b) 5/6 c) 11/12 d)1/6
17. An event is called statistically independent if
a) The probability of occurrence of one event is not affected by the occurrence of the other event.
b) The probability of occurrence of one event is affected by the occurrence of the other event.
c) The probability of occurrence of one event is affected by the occurrence of same event.
d) Non of these
Ans: Option a)
18. A fair coin is tossed 4 times, the probability that at least once head turns up is
a) 1/16
b) 15/16
c) 7/8
d) 1/8
19. The probability that Anil speaks truth is 4/5 while that of Bindu is 3/4, the probability that they are likely to contradict each other in stating the same fact is
a) 3/20
b) 4/5
c) 7/20
d) 1/5
20. Probability that at least one of the events A and B occur is 2/3 and probability that both the events A and B occur is 1/6. Then the value of P(Ac ) + P(Bc ) is
a) 7/6 b) 6/7 c) 6/5 d)5/6
21. Find the probability that a two-digit number selected randomly from all the two-digit numbers between 1 and 100 is divisible by neither 3 nor 5.
a) 8/15 b) 3/5 c) 2/5 d) 7/15
22. Find the probability that a two-digit number selected randomly from all the two-digit numbers between 1 and 100 is divisible by neither 3 nor 5.
a) 8/15 b)3/5 c)2/5 d)7/15
23. For a biased coin, when tossed 12 times, probability of getting exactly 7 heads is same as probability of getting exactly 6 heads. Then the probability of getting heads, when that coin is tossed once is --------------------
a) 5/13 b) 8/13 c) 6/13 d) 7/13
24. A bag contains 5 red balls 8 green balls. Two balls are drawn from the bag one after another without replacing the first ball. What is the probability that both balls are different color?
a) 10//39 b) 5/39 c) 5/13 d) 20/39
25. What is the probability that a quadratic equation ax2+bx+c has equal roots if a,b and c are distinct and are taken from {1,2,3,4,6,8,9}
a) 1/35 b) 2/35 c) 1/105 d) 2/105
26. An unbiased coin is tossed six times. The outcome of each toss is either head or tail. The probability of getting at least two heads is --------------
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