• #### 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

• 0.005
• 0.0103
• 0.0124
• 0.0057
• 0.0178

• 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

• 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

• 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

• 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

• 125
• 105
• 196
• 210
• 216

• 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

• 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

• 0
• 1
• 1/6
• 1/3
• None

• 1/27
• 1/6
• 1/9
• 1/8
• 1/5

• 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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