Zero Level
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Probability – 01
In each of the following experiments, describe the
sample space :
A coin is tossed two times.
A die is thrown two times.
A coin is tossed three times.
A coin is tossed four times.
A coin is tossed and then a die is rolled only in case a
head is shown on the coin.
Consider the experiment in which a coin is tossed
repeatedly until a head comes for the first time. Describe
the sample space.
2 boys and 2 girls are in Room X and 1 boy and 3 girls
in room Y. Specify the sample space for the experiment
in which a room is selected and then a person.
An experiment consists of recording boy-girl composition
of families with 2 children.
(i) What is the sample space, if we interested in knowing
whether it is a boy or girl in the order of their births ?
(ii) What is the sample space, if we are intereted in the
number of girls in a family ?
One die of red colour, one white and one of blue colour
are placed in a bag. One die is selected at random and
rolled, its colour and the number on its uppermost face
is noted. Describe the sample space.
An experiment consists of tossing a coin and then
tossing it second time, if a head occurs. If a tail occurs
on the first toss, then a die is tossed once. Find the
sample space.
A box contain 1 red and 3 identical white balls. Two balls
are drawn at random in succession without
replacement. W rite the sample space for this
experiment.
The numbers 1, 2, 3 and 4 are written separately on four
slips of paper. The slips are then put in a box and mixed
thoroughly. A person draws two slips from the box, one
after the other, without replacement. Describe the
sample space for the experiment.
A die is rolled. Let E be the event “die shows 4” and F be
the event “ die shows even number”. Are E and F mutually
exclusive ?
A die is thrown twice. Each time the number appearing
on it is recorded. Describe the events :
A : both numbers are odd.
B : both numbers are even.
C : sum of numbers is less than 6.
Describe A  B, A  B, A  C, A  C. W hich pairs of
events are mutually exclusive ?
An experiment involves rolling a pair of dice and recording
the numbers that come up. Describe the following
events :
A : the sum is greater than 8.
B : 2 occurs on either die.
C : the sum is at least 7 and a multiple of 3.
10/VII/22/ZLA/A/200
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Also, fine A  B, B  C and A  C.
Are (i) A and B mutually exclusive ?
(ii) B and C mutually exclusive ?
(iii) A and C mutually exclusive ?
A coin is tossed once. Then, if it turns up a head a die is
thrown once, if it turns up a tail it is tossed twice more.
Describe
(i) the sample space S of the experiment.
(ii) the event A “that exactly one head occurs”.
(iii) the event B “that at least two tails occur or a number
greater than 4 occurs”.
Three coins are tossed once. Let A be event “three
heads show”, B denote the event “two heads and one
tail show”, C denote the event “three tails show” and D
denote the event “a head shows on the first coin”.
Which events are :
(i) mutually exlusive ? (ii) simple ? (iii) compound ?
Two dice are thrown. The events A, B, C, D, E and F are
as follows :
A : getting an even number on the first die.
B : getting an odd number on the first die.
C : getting the sum of the numbers on the dice  5.
D : getting the sum of the number on the dice greater
than 5 but less than 10.
E : getting the sum of the numbers on the dice greater
than 10.
F : getting an odd number on one of the die. Describe
the events :
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(i) A'
(ii) B '
(iii) E '
(iv) A or B
(v) A and B (vi) B or C
(vii) B and C (viii) A and E
(ix) A or F (x) A and F
A coin is tossed once. Find the probability of getting a
head.
In a single throw of two dice, find the probability of
obtaining ‘a total of 8’.
A coin is tossed once. Find the probability of getting a
tail .
If S is the sample space of a certain experiment, what
can you say about P (S) ?
A coin is tossed twice. What is the probability that at
least one tail occurs ?
A die is thrown. Find the probability of :
(i) getting a prime number
(ii) getting a number  3
(iii) getting a number  4
(iv) getting a number more than 6
(v) getting a number less than 6
(vi) getting a number 5
(vii) getting an odd number
(viii) getting a number between 3 and 6
(ix) getting a multiple of 3
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If 2/11 is the probability then an event will happen, what
is the probability that it will not happen ?
In a simultaneous toss of two coins, find the probability
of :
(i) exactly 2 tails (ii) exactly one tail (iii) no tail.
In a single throw of two dice, determine the probability of
not getting the same number on the two dice.
In a single throw of two dice, find the probability of :
(i) getting a sum less than 6
(ii) getting a doublet of odd numbers
(iii) getting the sum as a prime number
In a single throw of two dice, find :
(i) P (an odd number on the first die and a 6 on the
second)
(ii) P (a number greater than 3 on each side)
(iii) P ( a total of 10)
(iv) P (a total greater than 8)
(v) P (a total of 9 or 11)
Three coins are tossed once. Find the probability of
getting :
(i) 3 heads
(ii) exactly 2 heads
(iii) at least 2 heads
(iv) at most 2 heads
(v) no neads
(vi) 3 tails
(vii) exactly 2 tails
(viii) no tails
(ix) exactly one tail
(x) a head on the first coin.
A card is drawn at random from a well-shuffled deck of
52 cards. Find the probability of getting :
(i) a king
(ii) heart
(iii) a seven of heart
(iv) a diamond
(v) a red card
(vi) a face card
(vii) a club
(viii) a non spade
(ix) a jack
(x) a queen.
A card is drawn at random from a well-shuffled deck of
52 cards. If A is the event of getting a red card and the
event B that a card is bearing a number greater than 2
but less than 9, find P (A) and P (B).
A card is drawn at random from a well-shuffled pack of
52 cards. What is the probability that the card bears a
number greater than 3 and less than 10 ?
A bag contain 9 red and 12 white balls.One ball drawn at
random.Find the probabitlity that the ball drawn is red.
From a bag containing 7 red and 5 black marbles, one
is drawn at random. What is probability of the marble
being :
(i) black ?
(ii) red ?
An urn contain 9 red, 7 white and 4 black balls. A ball is
drawn at random. What is the probability that the ball
drawn will be :
(i) red ?
(ii) white ?
(iii) black ? (iv) red or black
(v) white or black ?
(vi) not red ? (vii) not black ?
A bag contain 4 white and 5 black balls. A ball is drawn
ar random from the bag. Find the probability that the ball
drawn is white.
A bag contain 3 red balls bearing one of the numbers 1,
2 or 3 (one number on one ball); and 2 black balls bearing
the numbers 4 or 6. A ball is drawn, its number is noted
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and the ball is replaced in the bag. Then another ball is
drawn and its number is noted. Find the probability of
drawing :
(i) 2 on the first draw and 6 on the second draw
(ii) a number  2 on the first draw and 4 on the second
draw.
(iii) a total of 5.
If a letter is chosen at random from the English alphabet,
find the probability that the letter is (i) a vowel
(ii) a consonant.
What is the probability that an ordinary year has 53
tuesday ?
What is the probability that a leap year has 53 sunday ?
20 cards are numbered from 1 to 20. One card is then
drawn at random. What is the probability that the number
on the card will be :
(i) a multiple of 4 ?
(ii) not a multiple of 4 ?
(iii) odd ?
(iv) greater than 12 ?
(v) divisible by 5 ?
(vi) not a multiple of 6 ?
In a lottery a person chooses six different numbers at
random from 1 to 20, and if these six numbers match
with the six numbers already fixed by the lottery
committee, he wins the prize. What is the probability of
winning the prize in the game ?
What are odds in favour of getting a spade if the card is
drawn from a well-shuffled deck of 52 card ? What the
odds in favour of getting a king ?
A card is drawn from a well shuffled deck of 52 cards.
What are the odds in favour of getting a face card ?
The odds in favour of the occurrence of an event are
8 : 13; find the probability that the event will occur.
If the odd against the occurrence of an event are 4 : 7;
find the probability of the occurrence of the event.
The odds in favour of occurrence of an event are 5 : 13.
Find the probability that it will occur.
Two dice are thrown. Find :
(i) the odds in favour of getting the sum 6
(ii) the odds against getting the sum 7
If 5/14 is the probability of occurrence of an event, find
(i) the odds in favour of its occurrence
(ii) the odds against its occurrence
If 7/10 is the probability of occurrence of an event, what
is the probability that it does not occur ?
What is the probability that in a group of two people,
both will have the same birthday, assuming that there
are 365 days in a year and no one has his/her birthday
on 29th February ?
If P (A) = 3/5 and P (B) = 1/3, find :
P (A or B), if A and B are mutually exclusive events.
If A and B are two events such that P (A) = 1/4, P (B) =
1/2 and P ( A  B )  1 / 8 , find :
(i) P (A or B)
(ii) P (not A and not B).
If E1 and E 2 are two events associated with a random
experiment such that
P (E2 )  0.35, P (E1 or E2 )  0.85 and
P (E1 and E2 )  0.15, find P (E1) .
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Let A and B be two events associated with a random
experiment for which P(A) = 0.4, P(B) = 0.5 and P(A or B)
= 0.6 . Find P(A and B).
If A and B are two mutually exclusive events such that
P(A) = 1/2 and P(B) =1/3, find P(A or B).
In a random experiment, let A and B be events such P(A
or B) = 0.7, P (A and B) = 0.3 and P ( A )  0.4 , find P(B)
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and P (B ) .
If A and B are two events associated with a random
experiment such that P(A) = 0.25, P(B) = 0.4 and P(A or
B) = 0.5, find the values of
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(i) P(A and B)
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(ii) P ( A and B )
A and B are two events such that
P(A) = 0.42, P(B) = 0.48 and P(A and B) = 0.16.
Determine (i) P(not A)
(ii) P(not B) (iii) P(A or B).
From a well-shuffled pack of 52 cards, a card is drawn
at random. Find the probability of its being a king or a
queen.
From a well-shuffled pack of 52 cards, a card is drawn
at random. Find the probability of its being either a queen
or heart.
A card is drawn at random from a well-shuffled deck 52
cards. Find the probability that the card is a :
(i) king or a red card
(ii) club or a diamond
(iii) king or an ace
(iv) spade or a club
(v) neither a heart nor a king.
Two dice are rolled once. Find the probability that :
(i) the number on the two dice are different
(ii) the total is at least 3
(iii) the total is 6
(iv) the total is 7 or 9
(v) neither a doublet nor a total of 9 appear.
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A coin is tossed and a die is thrown. Find the probability
that the outcome will be a head or a number greater
than 4, or both.
A number is chosen from the number 1 to 100. Find the
probability of its being divisible by 4 or 6.
A die is thrown twice. What is the probability that at least
one of the two throws comes up with the number 4 ?
Two dice are thrown together. What is the probability
that the sum of the numbers on the two faces is neither
divisible by 3 nor by 4.
Two balls are drawn at random with replacement from a
box containing 10 black and 8 red balls. Find the
probability that :
(i) both balls are red
(ii) first ball is black and second is red.
(iii) one of them is black and other is red.
In a class, 30% of the students offered mathematics,
20% offered chemistry and 10% offered both. If a student
is selected at random, find the probability that he has
offered mathematics or chemistry.
The probability that a company executive will travel by
plane is 2/5 and that he will travel by train is 1/3. Find the
probability of his travelling by plane or train.
The probability that Bhuvesh passes in English is 2/3
and the probability that he passes in Hindi is 5/9. If the
probability of his passing both subject is 2/5, find the
probability that he will pass in atleast one of these
subjects.
In a town of 6000 people, 1200 are over 50 years old
and 2000 are females. It is known that 30% of the
females are over 50 years. What is the probability that a
randomly chosen individual from the town is either
female or over 50 years ?
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