Probability

The outcome of a random experiment results in either success or failure. If
the probability of success is twice the probability of failure, then the probability
of success is

Probability of sure event is  

The probability of selecting a queen of hearts when a card is drawn from a
pack of 52 playing cards is

The probability that a non-leap year will have 53 Sundays and 53 Mondays is

The probability that a leap year will have 53 Fridays or 53 Saturdays is

A card is drawn from a pack of 52 cards at random. The probability of
getting neither an ace nor a king card is

A fair die is thrown once. The probability of getting a prime or composite
Number is

Two dice are thrown simultaneously. The probability of getting a doublet is

A bag contains 5 black balls, 4 white balls and 3 red balls. If a ball is selected
at random, the probability that it is not red is

A bag contains 5 black balls, 4 white balls and 3 red balls. If a ball is selected
at random, the probability that it is not red is

If P(A) = 0.25, P(B) = 0.50, P(A ∪ B) = 0.14 then P(neither A nor B) =

If A and B are mutually exclusive events and S is the sample space such that
P(A) = 𝟏/𝟑  P(B) and S = A ∪ B, then P(A) =

There are 6 defective items in a sample of 20 items. One item is drawn at
random. The probability that it is a non-defective item is

If A and B are two events such that
P(A) = 0.25, P(B) = 0.05 and P(A ∩ B) = 0.14, then P(A∪B) =

The probability that a student will score centum in mathematics is 𝟒/𝟓. The probability that he will not score centum is

The probability that a student will score centum in mathematics is 𝟒/𝟓. The probability that he will not score centum is

If p is the probability of an event A, then p satisfies 

If ∅ is an impossible event, then P(∅)=

If ∅ is an impossible event, then P(∅)=

The probability that a new car will get an award for its design is 0.25, the
Probability that it will get an award for efficient use of fuel is 0.35 and the
Probability that it will get both the awards is 0.15. Find the probability that
(i) it will get at least one of the two awards;
(ii) it will get only one of the awards.

A card is drawn at random from a well-shuffled deck of 52 cards. Find
the probability that it will be a spade or a king.

In a class, 40% of the students participated in Mathematics-quiz, 30% in
Science-quiz and 10% in both the quiz programmes. If a student is selected at
random from the class, find the probability that the student participated in
Mathematics or Science or both quiz programmes.

A basket contains 20 apples and 10 oranges out of which 5 apples and 3
oranges are rotten. If a person takes out one fruit at random, find the probability
that the fruit is either an apple or a good fruit.

Two dice are rolled simultaneously. Find the probability that the sum of the
numbers on the faces is neither divisible by 3 nor by 4.

A bag contains 50 bolts and 150 nuts. Half of the bolts and half of the nuts are
rusted. If an item is chosen at random, find the probability that it is rusted
or that it is a bolt.

One number is chosen randomly from the integers 1 to 50. Find the
probability that it is divisible by 4 or 6.

If a die is rolled twice, find the probability of getting an even number
in the first time or a total of 8 .

A bag contains 12 balls out of which x balls are white.
(i) If one ball is drawn at random, what is the probability that it will be a white
ball. (ii) If 6 more white balls are put in the bag, the probability of drawing a
white ball will be twice that of in (i),then Find x.

Two dice are rolled and the product of the outcomes (numbers) are found.
What is the probability that the product so found is a prime number?

Three coins are tossed simultaneously. Find the probability of getting
(i) at least one head (ii) exactly two tails (iii) at least two heads.

Each individual letter of the word “ACCOMMODATION” is written in a
piece of paper, and all 13 pieces of papers are placed in a jar. If one piece of
paper is selected at random from the jar, find the probability that
(i) the letter „A‟ or „O‟ is selected
(ii) the letter „M‟ or „C‟ is selected.

A two digit number is formed with the digits 2, 5, 9 (repetition is allowed).
Find the probability that the number is divisible by 2 or 5.

A box contains 10 white, 6 red and 10 black balls. A ball is drawn at
random.Find the probability that the ball drawn is white or red.

Piggy bank contains 100 fifty- paise coins, 50 one-rupee coins, 20 two-rupees
coins and 10 five- rupees coins. One coin is drawn at random. Find the
probability that the drawn coin
(i) will be a fifty- paise coin (ii) will not be a five-rupees coin.

A bag consists of 100 shirts of which 88 are good, 8 have minor defects and 4
have major defects. A trader A will accept only the shirt which are good, but the
trader B will not accept the shirts which have major defects. One shirt is drawn
at random. What is the probability that it is acceptable by (i) A (ii) B ?.

Three dice are thrown simultaneously. Find the probability of getting the
same number on all the three dice.

A two digit number is formed with the digits 3, 5 and 7. Find the probability
that the number so formed is greater than 57 (repetition of digits is not allowed).
Solution:

20 cards are numbered from 1 to 20. One card is drawn at random. What is
the probability that the number on the card is
(i) a multiple of 4 (ii) not a multiple of 6.

A box contains 4 Green, 5 Blue and 3 Red balls. A ball is drawn at random.
Find the probability that the selected ball is
(i) Red in colour (ii) not Green in colour.

For a sightseeing trip, a tourist selects a country randomly from Argentina,
Bangladesh, China, Angola, Russia and Algeria. What is the probability that the
name of the selected country will begin with A ?

A number is selected at random from integers 1 to 100. Find the probability
that it is (i) a perfect square (ii) not a perfect cube.

A bag contains 6 white balls numbered from 1 to 6 and 4 red balls numbered
from 7 to 10. A ball is drawn at random. Find the probability of getting (i) an
even-numbered ball (ii) a white ball.

One card is drawn randomly from a well shuffled deck of 52 playing cards.
Find the probability that the drawn card is
(i) a Diamond (ii) not a Diamond (iii) not an Ace.

One card is drawn randomly from a well shuffled deck of 52 playing cards.
Find the probability that the drawn card is
(i) a Diamond (ii) not a Diamond (iii) not an Ace.

Two coins are tossed together. What is the probability of getting at most
one head.

Three rotten eggs are mixed with 12 good ones. One egg is chosen at random.
What is the probability of choosing a rotten egg?

A die is thrown twice. Find the probability of getting a total of 9.

A die is thrown twice. Find the probability of getting a total of 9.

A ticket is drawn from a bag containing 100 tickets. The tickets are numbered
from one to hundred. What is the probability of getting a ticket with a number
divisible by 10?

Which of the following arguments are correct and which are not correct? Give reasons for your answer.

(i) If two coins are tossed simultaneously there are three possible outcomes - - two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is.

(ii) If a die is thrown, there are two possible outcomes - - an odd number or an even number. Therefore, the probability of getting an odd number is.

A jar contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is. Find the number of blue balls in the jar.

A box contains 12 balls out of which x are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball?

If 6 more black balls are put in the box, the probability of drawing a black ball is now double of what it was before. Find x.

A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, determine the number of blue balls in the bag.

A die is numbered in such a way that its faces show the number 1, 2, 2, 3, 3, 6. It is thrown two times and the total score in two throws is noted. Complete the following table which gives a few values of the total score on the two throws:

What is the probability that the total score is

(i) even? (ii) 6? (iii) at least 6?

Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on

(i) the same day? (ii) consecutive days? (iii) different days?

A die is thrown twice. What is the probability that

(i) 5 will not come up either time?

(ii) 5 will come up at least once?

[Hint: Throwinga die twice and throwing two dice simultaneously are treated as the same experiment].

A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result i.e., three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.

Two dice, one blue and one grey, are thrown at the same time.

(i) Write down all the possible outcomes and complete the following table:

Event: Sum of two dice	2	3	4	5	6	7	8	9	10	11	12
Probability

(ii) A student argues that 'there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability

A lot consists of 144 ball pens of which 20 are defective and the others are good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that

(i) She will buy it?

(ii) She will not buy it?

Suppose you drop a die at random on the rectangular region shown in the given figure. What is the probability that it will land inside the circle with diameter 1 m?

A child has a die whose six faces shows the letters as given below:

The die is thrown once. What is the probability of getting (i) A? (ii) D?

A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears

(i) a two-digit number

(ii) a perfect square number

(iii) a number divisible by 5.

(i) A lot of 20 bulbs contain 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?

(ii) Suppose the bulb drawn in (i) is not defective and is not replaced. Now one bulb is drawn at random from the rest. What is the probability that this bulb is not defective?

12 defective pens are accidentally mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.

Five cards--the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random.

(i) What is the probability that the card is the queen?

(ii) If the queen is drawn and put aside, what is the probability that the second card picked up is (a) an ace? (b) a queen?

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting

(i) a king of red colour

(ii) a face card

(iii) a red face card

(iv) the jack of hearts

(v) a spade

(vi) the queen of diamonds

A die is thrown once. Find the probability of getting

(i) a prime number;

(ii) a number lying between 2 and 6;

(iii) an odd number.

A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see the given figure), and these are equally likely outcomes. What is the probability that it will point at

(i) 8?

(ii) an odd number?

(iii) a number greater than 2?

(iv) a number less than 9?

Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish (see the given figure). What is the probability that the fish taken out is a male fish?

A piggy bank contains hundred 50 p coins, fifty Rs 1 coins, twenty Rs 2 coins and ten Rs 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin

(i) Will be a 50 p coin?

(ii) Will not be a Rs.5 coin?

A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be (i) red? (ii) white? (iii) not green?

A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is (i) red? (ii) not red?

It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?

A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out

(i) an orange flavoured candy?

(ii) a lemon flavoured candy?

If P(E) = 0.05, what is the probability of 'not E'?

Which of the following cannot be the probability of an event?

Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football game?

Which of the following experiments have equally likely outcomes? Explain.

(i) A driver attempts to start a car. The car starts or does not start.

(ii) A player attempts to shoot a basketball. She/he shoots or misses the shot.

(iii) A trial is made to answer a true-false question. The answer is right or wrong.

(iv) A baby is born. It is a boy or a girl.

Complete the following statements:

(i) Probability of an event E + Probability of the event 'not E' = _______.

(ii) The probability of an event that cannot happen is _________. Such as event is called _________.

(iii) The probability of an event that is certain to happen is _________. Such as event is called ________.

(iv) The sum of the probabilities of all the elementary events of an experiment is _________.

(v) The probability of an event is greater than or equal to _______ and less than or equal to _______.