Class 10th Probability
PROBABILITY
Experimental or empirical probability P(E) of an event E is
Number of
trials
in which the event happened Total number
of trials
The theoretical probability (also called classical probability) of an event A, written as P(A), is defined as
Number of outcomes
favourable to A
Number of
all possible outcomes of
the experiment
Two or more events of an experiment, where occurrence of an event prevents occurrences of all
other events, are called
Mutually Exclusive Events.
COMPLIMENTARY EVENTS AND PROBABILITY
We denote the event 'not E' by E . This is called the complement event of event E.
So, P(E) + P(not E) = 1
i.e., P(E) + P(E) = 1, which gives us P( E) = 1 – P(E).
In general, it is true that for an event E, P(E ) = 1 – P(E)
FThe probability of an event which is impossible to occur is 0. Such an event is called an impossible event.
FThe probability of an event which is sure (or certain) to occur is 1. Such an event is called a sure event or a certain event.
FThe probability of an event E is a number P(E) such that 0 ≤ P (E) ≤ 1
FAn event having only one outcome is called an elementary event. The sum of the probabilities of all the elementary events of an experiment is 1.
DECK OF CARDS AND PROBABILITY
A deck of playing cards consists of 52 cards which are divided into 4 suits of 13 cards each. They are black spades (♠) red hearts (♥), red diamonds (♦) and black clubs (♣).
The cards in each suit are Ace, King, Queen, Jack, 10, 9, 8, 7, 6, 5, 4, 3 and 2. Kings, Queens and Jacks are called face cards.
Questions
Que1. The probability that it will rain tomorrow is 0.85. What is the probability that it will not rain tomorrow?
Que2. A die is thrown. Find the
probability of getting:
(i) a prime number
(ii) 2 or 4
(iii) a multiple of 2 or 3
(iv) an even prime number
(v) a number greater
than 5
(vi) a number lying between 2 and 6
Que3. In a simultaneous throw
of a pair of dice, find the probability of getting:
(ii) a doublet
(iii) a doublet of prime numbers
(iv) a doublet of odd numbers
(v) a sum greater than 9
(vi) an even number on first
(vii) an even number on one and a multiple of 3 on the other
(viii) neither 9 nor 1 1 as the sum of the numbers on the faces
(xi) a sum more than 7
(xii) at least once
Que4. Three coins are tossed together. Find the probability of getting:
(i) exactly two heads
(ii) at least two heads
(iii) at least one head and one
tail
(iv) no tails
Que5. What is the probability that an
ordinary year has 53 Sundays?
Que6. What is the probability that a leap year has 53 Sundays
and 53 Mondays?
Que7. A and B throw a pair of dice. If A throws 9,
find B’s chance of throwing
a higher number.
Que8. Two unbiased dice are thrown.
Find the probability that the total
of the numbers on the dice is greater than 10.
Que9. A card is drawn at random from a pack of 52 cards. Find the probability that card drawn is
|
(i) |
a black king |
(ix) |
other than an ace |
|
(ii) |
either a black card or a king |
(x) |
a ten |
|
(iii) |
black and a king |
(xi) |
a spade |
|
(iv) |
a jack,
queen or a king |
(xii) |
a black card |
|
(v) |
neither a heart
nor a king |
(xiii) |
the seven of clubs |
|
(vi) |
spade or an ace |
(xiv) |
jack |
|
(vii) |
neither an
ace nor a king |
(xv) |
the ace ofspades |
|
(viii) |
Neither a
red card nor a queen. |
(xvi) |
a queen |
Que10. In a lottery
of 50 tickets numbered 1 to 50, one ticket is drawn. Find the probability that the drawn ticket bears a prime number.
Que11. An urn contains 10 red and 8 white
balls. One ball is drawn
at random. Find the probability that the ball drawn is white.
Que12. A bag contains 3 red balls, 5 black balls and 4 white balls. A ball is drawn at random
from the bag. What is the probability that the ball drawn is:
(i) White
(ii) Red
(iii) Black
(iv) Not red
Que13. What is the probability that a number selected from the numbers
1, 2, 3, ..., 15 is a multiple of 4?
Que14. A bag contains 6 red, 8 black and 4 white balls. A ball is drawn at random.
What is the probability that ball drawn is not black?
Que15. A bag contains 5 white and 7 red balls. One ball is drawn at random. What is the probability that ball drawn is white?
Que16. Tickets numbered
from 1 to 20 are mixed up and a ticket is drawn at random. What is the probability that the ticket drawn has
a number which is a multiple of 3 or 7?
Que17. In a lottery there
are 10 prizes and 25 blanks. What is the probability of getting a prize?
Que18. If the probability of winning a game is 0.3, what is the probability of losing it?
Que19. A bag contains 5 black, 7 red and 3 white balls. A ball is drawn from the bag at random.
Find the probability that the ball drawn is:
(i) Red (ii) black or white (iii) not black
Que20. A bag contains 4 red, 5 black and 6 white balls. A ball is drawn from the bag at random. Find the probability that the ball
drawn is:
(i) White
(ii) Red
(iii) Not black
(iv) Red or white
Que21. A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability?
(i)
that the sum of the two numbers
that turn up is 8?
(ii)
of obtaining a total of 6?
Que22. One card is drawn from a well shuffled
deck of 52 cards. Find the probability of getting:
(i)
a king of red suit
(ii)
a face card
(iii)
a red face card
(iv)
a queen of black suit
(v)
a jack of hearts
(vi)
a spade
Que23. Five cards—ten, jack, queen, king,
and an ace of diamonds
are shuffled face downwards. One card is picked at
random.
(i) What is the probability that the card is a queen?
(ii) If a king is drawn first and put aside, what is the probability that the second card picked up is the ace?
Que24. 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)
Black
Que 25. A bag contains cards
which are numbered
from 2 to 90. A card is drawn at random from the bag. Find the probability that
it bears.
(i)
a two digit number
(ii)
a number which is a perfect square
Que 26. Two customers are visiting a particular shop in the same week (Monday to Saturday).
Each is equally likely to visit the shop on any one day
as on another. What is the probability
that both will visit the shop on:
(i)
the same day? (ii) different days? (iii) consecutive days?
Que 27. In a class,
there are 18 girls and 16 boys. The class teacher wants to choose one pupil for
class monitor. What she does, she writes the name of each pupil on a card and
puts them into a basket
and mixes thoroughly. A child is asked to pick one card from the basket. What is the probability that the
name written on the card is:
(i)
the name of a girl
(ii)
the name of a boy
Que 28. Why is tossing a coin considered to be a fair way of deciding
which team should choose
ends in a game of cricket?
Que 29. What is the probability that a number selected at random
from the number
1,2,2,3,3,3, 4, 4, 4, 4 will
be their average?
Que 30. The faces
of a red cube and a yellow
cube are numbered
from 1 to 6. Both cubes are rolled.
What is the probability that the top face of each cube will have the same
number?
Que 31.
The probability of
selecting a green marble at random
from a jar that contains only green,
white and yellow marbles
is 1. The probability of selecting a white marble at random from
4
the same jar is 1 . If this jar contains 10 yellow marbles.
What is the total number of
3
marbles in the jar?
Que32. There are
30 cards, of same size, in a bag on which numbers 1 to 30 are written. One card
is taken out of the bag at random. Find the probability that the number
on the selected card is not divisible by 3.
Que33. A bag contains 5 red, 8 white and 7 black
balls. A ball is
drawn at random
from the bag.
Find the probability that the drawn ball is
(i)
red or white
(ii)
not black
(iii)
neither white nor black.
Que34. Find the probability that a number selected from the number 1 to 25 is not a prime number
when each of the given numbers is equallylikely to be selected.
Que35. A bag contains 8 red, 6 white and 4 black
balls. A ball is
drawn at random
from the bag.
Find the probability that the drawn ball is
(i)
Red or white
(ii)
Not black
(iii)
Neither white nor black
36. Find the probability that a
number selected at random
from the numbers
1, 2, 3, ..., 35 is a
Prime number (ii) Multiple
of 7 (iii) Multiple
of 3 or 5
37.
From a pack of 52 playing cards Jacks, queens, kings and aces of red
colour are removed. From the remaining, a card is drawn at random. Find the probability that the card drawn
is
(i)
A black queen
(ii)
A red card
(iii)
A black jack
(iv)
a picture card (Jacks, queens
and kings are picture cards)
38. 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?
39. It is given that m 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?
40. 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?
41. (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
(a)
is not defective and nõt replaced.
Now bulb is drawn at random from the rest.
What is the probability that this bulb is not defective?
42. A box contains 90 discs which
are numbered from 1 to 90. If one discs 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.
43. A lot consists of 144 ball pens of which 20 are defective
and others good. Nun 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?
44. 12 defective
pens are accidently mixed with 132 good ones. It is not possible
to just look at 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 good one.
45. 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 a side,
what is the probability that the second
card picked up is
a. an ace?
b. a queen?
(iii)
46. Harpreet tosses
two different coins
simultaneously (say, one is of Re 1 and other
of Rs 2). What is the probability that he gets at least one head?
47. Two dice,
one blue and one grey, are thrown
at the same time. Complete
the following table:
|
Event: ‘Sum on two dice’ |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
|
Probability |
|
|
|
|
|
|
|
|
|
|
|
From the above table a student argues that there are 1 1 possible outcomes 2,3,4,5,6,7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability j-j . Do you agree with this argument?
48. Cards marked with numbers
13, 14, 15,.... ,
60 are placed in a box and
mixed thoroughly.
One card is drawn at random from the box. Find the probability that number on the card drawn is
(i)
divisible by 5
(ii)
a number is a perfect
squar
49. A bag contains 6 red balls and some blue balls. If
the probability of drawing a blue ball the bag is twice that of a red ball,
find the number of blue balls in the bag.
50. A bag contains tickets
numbered 11, 12, 13,..., 30. A ticket
is taken out from the bag at random. Find the probability that the
number on the drawn ticket
(i)
is a multiple of 7
(ii)
is greater than 15
and a multiple of 5.
51. The king,
queen and jack of clubs
are removed from a deck of 52 playing cards and the remaining cards are shuffled. A card
is drawn from the remaining cards. Find the probability of getting a card of-
(i)
heart
(ii)
queen
(iii)
clubs.
52. Two dice are thrown
simultaneously. What is the
probability that:
(i)
5 will not come up on either of them?
(ii)
5 will come up on at least one?
