Quiz  /  Probability Bank PO MCQ Questions With Answers

  • 1. 
    One-third of 12 oranges got rotten. If 4 oranges are taken out randomly, what is the probability that all orange are rotten?

  • 14/995
  • 1/495
  • 16/495
  • 8/495
  • None of these

  • 2. 
    One card is drawn from a pack of 52 cards, each of the 52 cards being equally likely to be drawn find the probability the card drawn is black.

  • 1/2
  • 2/3
  • 3/4
  • 2/5
  • None of these

  • 3. 
    A factory produces four different types of products, P, Q, R and S. The chances that a random piece of products P, Q, R and S is found to be defective are 20%, 30%, 5% and 10%, respectively. During an inspection, one piece of each product is randomly selected. What is the probability that exactly three of them are found to be defective?

  • 0.005
  • 0.0103
  • 0.0124
  • 0.0057
  • 0.0178

  • 4. 
    A bag contains 20 yellow balls, 10 green balls, 5 white balls, 8 black balls, and 1 red ball. How many minimum balls one should pick out so that to make sure the he gets at least 2 balls of same color.

  • 7 balls
  • 4 balls
  • 8 balls
  • 6 balls
  • 9 balls

  • 5. 
    A dice is rolled three times and sum of three numbers appearing on the uppermost face is 15. What is the chance that the first roll was four?

  • 1/216
  • 2/69
  • 1/5
  • 3/71
  • None of these

  • 6. 
    A fair coin is tossed 10 times. What is the probability that only the first two tosses will yield tails?

  • \({1 \over 2}\)
  • \({\left( {{1 \over 2}} \right)^2}\)
  • \({}^{10}{C_2}{\left( {\frac{1}{2}} \right)^2}\)
  • \({\left( {\frac{1}{2}} \right)^{10}}\)
  • \({\left( {\frac{1}{2}} \right)^8}\)

  • 7. 
    The following question has three statements. Study the question and the statements to decide which of the statement(s) is/are necessary to answer the question. A committee having 2 Hindi teachers and 2 English teachers is to be formed from some ‘Hindi teachers’ and ‘English teachers’. The probability of doing so is 3/5. Find the total number of Hindi and English teachers. Statement I: Number of ways to choose 2 teachers out of total teachers is 15 Statement II: Number of ways to choose 2 Hindi teachers out of total Hindi teachers is 3 Statement III: Number of English teachers is 3

  • Statement (I) alone is sufficient
  • Statement (II) alone is sufficient
  • Statement (III) alone is sufficient
  • Each of the statements alone is sufficient
  • Statement (II) and (III) together are sufficient

  • 8. 
    A small spherical substance was accidently dropped into a cylindrical vessel of height 42 cm and radius 30 cm filled with water. A small cylindrical glass of height 7 cm and radius 5 cm was used to take some water from it. What is the probability that the small spherical substance gets transferred to the glass?

  • 1/6
  • 1/36
  • 1/216
  • 1/24
  • 1/30

  • 9. 
    The odds against an event A are 5:3 and odds in favor of another independent event B and 6:5. The chances that neither A nor B occurs is

  • 52/88
  • 25/88
  • 10/88
  • 12/88
  • None of these

  • 10. 
    A speaks truth in 75% cases and B speaks truth in 25% cases. A car accident takes place at highway. What is the probability that they will report this event truly or both of them will not speak truth?

  • \(\frac{3}{{16}}\)
  • \(\frac{3}{{8}}\)
  • \(\frac{5}{{8}}\)
  • \(\frac{5}{{16}}\)
  • None

  • 11. 
    A box contains 100 round discs, 50 square - shaped discs and 30 triangular discs. All the discs are made up of iron and have an equal probability of getting attracted by a magnet. If a magnet which can attract only one disc in one pass and the disc is passed over them twice. What is the probability that both times a triangular disc is attracted? The disc attracted in one pass does not fall into box again, however each time a square shaped disc is kept into the box.

  • \(\frac{{29}}{{180}}\)
  • \(\frac{{29}}{{1074}}\)
  • \(\frac{1}{{36}}\)
  • \(\frac{{29}}{{1080}}\)
  • None

  • 12. 
    In a box, 4 coins of ten rupees, 2 coins of five rupees, 2 coins of two rupees and 2 coins of one rupee are put. Now, three coins are taken out randomly. What is the probability that the amount drawn is 12 rupees?

  • 1/5
  • 1/6
  • 3/16
  • 1/10
  • 1/20

  • 13. 
    All black face cards are removed from a pack of playing cards. The remaining cards are well shuffled and then two cards are drawn at random one after the other without replacement. Find the probability that the first card is black and the second one is red?

  • \(\frac{{130}}{{529}}\)
  • \(\frac{{52}}{{207}}\)
  • \(\frac{1}{4}\)
  • \(\frac{{100}}{{529}}\)
  • None

  • 14. 
    Five letters are sent to different persons and addresses on the five envelopes are written ।at random. The probability that all the letters do not reach the correct destiny is

  • 44/120
  • 1/120
  • 1/5
  • Cannot be determined
  • None of these

  • 15. 
    There are 49 cards in a box numbered from 1 to 49. Every card is numbered with only 1 number. Probability of picking up a card, the number printed on which is a multiple of 5 but not that of 10 or 15 is.

  • 2/49
  • 3/49
  • 4/49
  • 5/49
  • None of these

  • 16. 
    Mark and Matt are born in two consecutive months of 2011. What is the probability that the numbers of months in which they are born have same number of days?

  • 1/22
  • 1/11
  • 2/33
  • 1/9
  • 1/6

  • 17. 
    If the probability that A will live 15 years is \(\frac{7}{8}\) and that B will live 15 years is \(\frac{9}{{10}}\), then what is the probability that both will live 15 years?

  • \(\frac{1}{{20}}\)
  • \(\frac{{63}}{{80}}\)
  • \(\frac{{1}}{{5}}\)
  • Cannot be determined
  • None of these

  • 18. 
    A problem is given to three persons and their chances of solving it are 1/3, 1/4, 1/5 respectively. This probability that none will solve it is

  • \(\frac{1}{3} \times \frac{1}{4} \times \frac{1}{5}\)
  • \(\frac{2}{3} \times \frac{3}{4} \times \frac{4}{5}\)
  • \(1 - \frac{2}{3} \times \frac{3}{4} \times \frac{4}{5}\)
  • \(\frac{1}{3} + \frac{1}{4} + \frac{1}{5}\)
  • None of these

  • 19. 
    From a railway station, trains leave for every 15 minutes and 25 minutes to city A and city B respectively. First train to city A and city B start at 9 am and 10.15 am respectively. If a man arrives to the station in between 11.25 am and 12.25 pm then the probability of getting train for city A is:

  • 4/7
  • 1/15
  • 3/5
  • 2/5
  • None of these

  • 20. 
    The probability that a randomly chosen ball is defective is 1/3. The probability that a randomly chosen ball is red is 2/7. Out of a total of N balls, 100 balls are there that are neither defective nor red. Find the value of N.

  • 125
  • 105
  • 196
  • 210
  • 216

  • 21. 
    Cards numbered from 107 to 1006 are put in a bag. A card is drawn from it at random. Find the probability that the number on the card is not divisible both by 11 and 37?

  • 0.998
  • 0.105
  • 0.107
  • 0.103
  • None

  • 22. 
    Trimsy speaks the truth 2 out of 9 times. On selecting a card randomly from a pack of cards, she reports that it is either king or ace. Find the probability that it is actually king or ace.

  • 45/91
  • 4/117
  • 25/91
  • 32/117
  • None of these

  • 23. 
    Around a round table, 13 persons are sitting on 13 chairs. Harry is one among them. A person is chosen randomly from them (other than Harry). What is the probability that there will be exactly 2 persons between Harry and the chosen person?

  • 1/3
  • 1/6
  • 1/5
  • 2/13
  • 1/8

  • 24. 
    What is the probability of solving a given problem if three students (A, B and C), try it independently, with respective probabilities \(\frac{4}{7},\frac{3}{8}\;and\frac{1}{2}?\;\)

  • \(\frac{{97}}{{112}}\)
  • \(\frac{{95}}{{112}}\)
  • \(\frac{{97}}{{111}}\)
  • \(\frac{{97}}{{125}}\)
  • None of these

  • 25. 
    In a city of 5 million people, there are 1 million politicians. 10 persons are selected randomly from the city. What is the probability that at most three of them are politicians?

  • 1.688 × (4/5)7
  • 2.442 × (4/5)7
  • 2.096 × (4/5)7
  • 4.192 × (4/5)7
  • 6.288 × (4/5)7

  • 26. 
    Six cards King, Queen, Jack, Ace, the five and the nine of spades from a set of cards are well shuffled. One card is picked up at random. Then it is kept aside and other card is drawn. What is the probability that both the cards are Jacks of spade?

  • 0
  • 1
  • 1/6
  • 1/3
  • None

  • 27. 
    Three letters are written to different persons and addresses on the envelopes are also written. Without looking at the addresses, the letter are put into the envelope, the probability that letters to into the right envelops is

  • 1/27
  • 1/6
  • 1/9
  • 1/8
  • 1/5

  • 28. 
    Two dices are taken. On faces of first dice, numbers from 1 to 6 are written. On second dice, six consecutive natural numbers are written. They are thrown together. What is the probability that the sum of outcomes when divided by 3 will leave a remainder of 1?

  • 1/2
  • 1/3
  • 1/4
  • 1/6
  • 3/5

  • 29. 
    A room contains 3 red, 5 green and 4 blue chairs. Two chairs are picked and are put in the lawn. What is the probability that none of the chairs picked is blue?

  • 14/33
  • 9/22
  • 1/6
  • 1/3
  • None of these
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