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Q.1
The probability that a number selected at random from the first 50 natural numbers is a composite number is -
$$\frac{{21}}{{25}}$$
$$\frac{{17}}{{25}}$$
$$\frac{{4}}{{25}}$$
$$\frac{{8}}{{25}}$$
Q.2
If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is -
$$\frac{{19}}{{52}}$$
$$\frac{{17}}{{52}}$$
$$\frac{{5}}{{13}}$$
$$\frac{{4}}{{13}}$$
Q.3
Three unbiased coins are tossed. What is the probability of getting at least 2 tails?
0.75
0.5
0.25
0.2
Q.4
A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that at least one bulb is good.
$$\frac{{6}}{{63}}$$
$$\frac{{2}}{{63}}$$
$$\frac{{125}}{{126}}$$
$$\frac{{1}}{{126}}$$
Q.5
From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is -
$$\frac{{1}}{{26}}$$
$$\frac{{3}}{{52}}$$
$$\frac{{15}}{{26}}$$
$$\frac{{11}}{{26}}$$
Q.6
A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is -
$$\frac{{8}}{{15}}$$
$$\frac{{2}}{{5}}$$
$$\frac{{3}}{{5}}$$
$$\frac{{7}}{{15}}$$
Q.7
If x is chosen at random from the set {1, 2, 3, 4} and y is to be chosen at random from the set {5, 6, 7}, what is the probability that xy will be even?
$$\frac{{5}}{{6}}$$
$$\frac{{1}}{{6}}$$
$$\frac{{1}}{{2}}$$
$$\frac{{2}}{{3}}$$
Q.8
From a bag containing 4 white and 5 black balls a man drawn 3 balls at random. What are the odds against these balls being black?
$$\frac{{5}}{{37}}$$
$$\frac{{37}}{{5}}$$
$$\frac{{11}}{{13}}$$
$$\frac{{13}}{{37}}$$
Q.9
A bag contains 12 white and 18 black balls. Two balls are drawn in succession without replacement.
What is the probability that first is white and second is black?
$$\frac{{18}}{{145}}$$
$$\frac{{18}}{{29}}$$
$$\frac{{36}}{{135}}$$
$$\frac{{36}}{{145}}$$
Q.10
A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
$$\frac{{4}}{{9}}$$
$$\frac{{5}}{{9}}$$
$$\frac{{7}}{{9}}$$
$$\frac{{8}}{{9}}$$
Q.11
Two brother X and Y appeared for an exam. Let A be the event that X is selected and B is the event that Y is selected.
The probability of A is $$\frac{{1}}{{7}}$$ and that of B is $$\frac{{2}}{{9}}$$. Find the probability that both of them are selected.
$$\frac{{1}}{{63}}$$
$$\frac{{2}}{{35}}$$
$$\frac{{2}}{{63}}$$
$$\frac{{9}}{{14}}$$
Q.12
A coin is tossed live times. What is the probability that there is at the least one tail?
$$\frac{{31}}{{32}}$$
$$\frac{{1}}{{16}}$$
$$\frac{{1}}{{2}}$$
$$\frac{{1}}{{32}}$$
Q.13
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
$$\frac{{1}}{{455}}$$
$$\frac{{2}}{{455}}$$
$$\frac{{1}}{{91}}$$
$$\frac{{4}}{{455}}$$
Q.14
In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?
$$\frac{{5}}{{21}}$$
$$\frac{{5}}{{14}}$$
$$\frac{{9}}{{14}}$$
$$\frac{{16}}{{21}}$$
Q.15
A number X is chosen at random from the numbers -3, -2, -1, 0, 1, 2, 3. What is the probability that $$|X| < 2$$
$$\frac{{5}}{{7}}$$
$$\frac{{3}}{{7}}$$
$$\frac{{3}}{{5}}$$
$$\frac{{1}}{{3}}$$
Q.16
A bag contains 5 red and 3 green balls. Another bag contains 4 red and 6 green balls. If one ball is drawn from each bag.
Find the probability that one ball is red and one is green.
$$\frac{{19}}{{20}}$$
$$\frac{{17}}{{20}}$$
$$\frac{{8}}{{10}}$$
$$\frac{{21}}{{40}}$$
Q.17
There are four hotels in a town. If 3 men check into the hotels in a day then what is the probability that each checks into a different hotel?
$$\frac{{6}}{{7}}$$
$$\frac{{1}}{{8}}$$
$$\frac{{3}}{{8}}$$
$$\frac{{5}}{{9}}$$
Q.18
A speaks truth in 75% of cases and B in 80% of cases. In what percent of cases are they likely to contradict each other in narrating the same event?
35%
5%
45%
22.5%
Q.19
Find the probability that in a random arrangement of the letters of the word 'UNIVERSITY' the two I's come together.
$$\frac{1}{7}$$
$$\frac{3}{5}$$
$$\frac{5}{11}$$
$$\frac{1}{5}$$
Q.20
Four cards are drawn at random from a pack of 52 playing cards. Find the probability of getting all the four cards of the same suit.
$$\frac{{13}}{{270725}}$$
$$\frac{{91}}{{190}}$$
$$\frac{{178}}{{20825}}$$
$$\frac{{44}}{{4165}}$$
Q.21
A card is drawn from a pack of 52 cards. The card is drawn at random. What is the probability that it is neither a spade nor a Jack?
$$\frac{{4}}{{13}}$$
$$\frac{{2}}{{13}}$$
$$\frac{{6}}{{13}}$$
$$\frac{{9}}{{13}}$$
Q.22
An urn contains 6 red, 5 blue and 2 green marbles. If 2 marbles are picked at random, what is the probability that both are red?
$$\frac{6}{{13}}$$
$$\frac{{5}}{{26}}$$
$$\frac{{5}}{{13}}$$
$$\frac{{7}}{{26}}$$
Q.23
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
$$\frac{{3}}{{22}}$$
$$\frac{{4}}{{21}}$$
$$\frac{{2}}{{21}}$$
$$\frac{{1}}{{14}}$$
Q.24
10 books are placed at random in a shelf. The probability that a pair of books will always be together is -
$$\frac{{1}}{{10}}$$
$$\frac{{9}}{{10}}$$
$$\frac{{1}}{{5}}$$
$$\frac{{3}}{{10}}$$
Q.25
Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is-
$$\frac{{3}}{{20}}$$
$$\frac{{29}}{{34}}$$
$$\frac{{47}}{{100}}$$
$$\frac{{13}}{{102}}$$
Q.26
An urn contains 6 red, 4 blue, 2 green and 3 yellow marbles. If three marbles are picked up at random, what is the probability that 2 are blue and 1 is yellow ?
$$\frac{{13}}{{35}}$$
$$\frac{{1}}{{5}}$$
$$\frac{{18}}{{455}}$$
$$\frac{{7}}{{15}}$$
None of these
Q.27
If a number is chosen at random from the set {1, 2, 3, ......., 100}, then the probability that the chosen number is a perfect cube is -
$$\frac{{1}}{{25}}$$
$$\frac{{1}}{{2}}$$
$$\frac{{4}}{{13}}$$
$$\frac{{1}}{{10}}$$
Q.28
In a race where 12 cars are running, the chance that car X will win is $$\frac{1}{6},$$ that Y will win is $$\frac{{1}}{{10}}$$ and that Z will win is $$\frac{{1}}{{8}}$$. Assuming that a dead heat is impossible. Find the chance that one of them will win.
$$\frac{{47}}{{120}}$$
$$\frac{{1}}{{480}}$$
$$\frac{{1}}{{160}}$$
$$\frac{{1}}{{240}}$$
Q.29
A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd?
$$\frac{{1}}{{2}}$$
$$\frac{{3}}{{4}}$$
$$\frac{{3}}{{8}}$$
$$\frac{{1}}{{8}}$$
Q.30
The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on at least one ticket is -
0.4869
0.5904
0.6234
0.5834
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