Multiple choice questions with answers / choose the correct answer with answers - Maths Book back 1 mark questions and answers with solution for Exercise Problems: Mathematics : Introduction to Probability Theory

**Introduction to Probability Theory (Mathematics)**

**Choose the correct or
most suitable answer from the given four alternatives**

(1) Four persons are
selected at random from a group of 3 men, 2 women and 4 children. The
probability that exactly two of them are children is

(1) 3/4

(2) 10/23

(3) 1/2

**(4) 10/21**

**Ans: (4)**

*Solution*

(2) A number is selected
from the set { 1, 2, 3,..., 20 }. The probability that the selected number is
divisible by 3 or 4 is

(1) 2/5

(2) 1/8

**(3) 1/2 **

(4) 2/3

**Ans: (3)**

*Solution*

(3) A, B, and C try to
hit a target simultaneously but independently. Their respective probabilities
of hitting the target are 3/4 , 1/2 , 8/5 . The probability that the target is
hit by A or B but not by C is

**(1) 21 /64**

(2) 7/32

(3) 9/64

(4) 7/8

**Ans: (1)**

*Solution*

(4) If A and B are any
two events, then the probability that exactly one of them occur is

(3) P( A ) + P( B ) âˆ’ P(
A âˆ© B )

(4) P ( A) + P ( B ) + 2
P ( A âˆ© B)

**Ans: (2)**

*Solution*

(5) Let A and B be two events such that P = 1/6 , P ( A âˆ© B) = 1/4 and P () = 1/4 . Then the events A and B are

(1) Equally likely
but not independent

**(2) Independent but not
equally likely**

(3) Independent
and equally likely

(4) Mutually inclusive
and dependent

**Ans: (2)**

*Solution*

(6) Two items are chosen
from a lot containing twelve items of which four are defective, then the
probability that at least one of the item is defective

**(1) 19/33 **

(2) 17/33

(3) 23/33

(4) 13/33

**Ans: (1)**

*Solution*

(7) A man has 3 fifty
rupee notes, 4 hundred rupees notes and 6 five hundred rupees notes in his
pocket. If 2 notes are taken at random, what are the odds in favour of both
notes being of hundred rupee denomination?

**(1) 1:12 **

(2) 12:1

(3) 13:1

(4) 1:13

**Ans: (1)**

*Solution*

(8) A letter is taken at
random from the letters of the word â€˜ASSISTANTâ€™ and another letter is taken at
random from the letters of the word â€˜STATISTICSâ€™. The probability that the
selected letters are the same is

(1) 7/45

(2) 17/90

(3) 29/90

**(4) 19/90**

**Ans: (4)**

*Solution*

(9) A matrix is chosen
at random from a set of all matrices of order 2, with elements 0 or 1 only. The
probability that the determinant of the matrix chosen is non zero will be

(1) 3/16

**(2) 3/8 **

(3) 1/4

(4) 5/8

**Ans: (2)**

*Solution*

(10) A bag contains 5
white and 3 black balls. Five balls are drawn successively without replacement.
The probability that they are alternately of different colours is

(1) 3/14

(2) 5/14

**(3) 1/14 **

(4) 9/14

**Ans: (3)**

*Solution*

(11) If A and B
are two events such that A âŠ‚ B and P (B) â‰ 0, then
which of the following is correct?

(1) P ( A / B) = P ( A)
/ P ( B)

(2) P ( A / B ) < P(
A)

**(3) P ( A / B ) â‰¥ P(
A) **

(4) P ( A / B ) >
P(B)

**Ans: (3)**

(12) A bag
contains 6 green, 2 white, and 7 black balls. If two balls are drawn
simultaneously, then the probability that both are different colours is

**(1) 68/105 **

(2) 71/105

(3) 64/105

(4) 73/105

**Ans: (1)**

*Solution*

(13) If *X* and *Y*
be two events such that P ( X / Y ) = 1/2 , P ( Y / X ) = 1/3 and P ( X âˆ© Y ) =
16 , then P ( X âˆªY ) is

(1) 1/3

(2) 2/5

(3) 1/6

**(4) 2/3 **

**Ans: (4)**

*Solution*

(14) An urn contains 5
red and 5 black balls. A ball is drawn at random, its colour is noted and is
returned to the urn. Moreover, 2 additional balls of the colour drawn are put
in the urn and then a ball is drawn at random. The probability that the second
ball drawn is red will be

(1) 5/12

**(2) 1/2 **

(3) 7/12

(4) 1/4

**Ans: (2)**

*Solution*

(15) A number x is
chosen at random from the first 100 natural numbers. Let *A* be the event
of numbers which satisfies [(x âˆ’ 10)(x âˆ’ 50)] / [x âˆ’ 30 ] â‰¥ 0 , then P ( A) is

(1) 0.20

(2) 0.51

**(3) 0.71 **

(4) 0.70

**Ans: (3)**

*Solution*

(16) If two events A and
B are independent such that P ( A) = 0.35 and P ( A âˆª
B) = 0.6 , then P (B) is

**(1) 5/13 **

(2) 1/13

(3) 4/13

(4) 7/13

**Ans: (1)**

*Solution*

(17) If two events *A*
and *B* are such that P () = 3/10 and P ( A âˆ© ) = 1/2 , then
P ( A âˆ© B) is

(1) 1/2

(2) 1/3

(3) 1/4

**(4) 1/5 **

**Ans: (4)**

*Solution*

(18) If A and B are two
events such that P (A)= 0.4, P ( B) = 0.8 and P ( B / A) = 0.6 , then P ( âˆ© B) is

(1) 0.96

(2) 0.24

**(3) 0.56 **

(4) 0.66

**Ans: (3)**

*Solution*

(19) There are three
events *A, B* and *C* of which one and only one can happen. If the
odds are 7 to 4 against A and 5 to 3 against *B*, then odds against *C*
is

(1) 23: 65

**(2) 65: 23**

(3) 23: 88

(4) 88: 23

**Ans: (2)**

*Solution*

(20) If a and b are
chosen randomly from the set {1,2,3,4}with replacement, then the probability of
the real roots of the equation x^{2} + ax + b = 0 is

(1) 3/16

(2) 5/16

**(3) 7/16 **

(4) 11/16

**Ans: (3)**

*Solution*

(21) It is given that
the events A and B are such that P( A) = 1/4 , P ( A / B) = 1/2 and P ( B / A)
= 2/3 . Then P(B) is

(1) 1/6

**(2) 1/3**

(3) 2/3

(4) 1/2

**Ans: (2)**

*Solution*

(22) In a certain
college 4% of the boys and 1% of the girls are taller than 1.8 meter. Further
60% of the students are girls. If a student is selected at random and is taller
than 1.8 meters, then the probability that the student is a girl is

(1) 2/11

**(2) 3/11 **

(3) 5/11

(4) 7/11

**Ans: (2)**

*Solution*

(23) Ten coins are
tossed. The probability of getting at least 8 heads is

(1) 7/64

(2) 7/32

(3) 7/16

**(4) 7/128**

**Ans: (4)**

*Solution*

(24) The
probability of two events A and B are 0.3 and 0.6 respectively. The probability
that both A and B occur simultaneously is 0.18. The probability that neither A
nor B occurs is

(1) 0.1

(2) 0.72

(3) 0.42

**(4) 0.28**

**Ans: (4)**

*Solution*

(25) If *m* is a
number such that *m* â‰¤ 5, then the probability that quadratic equation 2*x*^{2}
+ 2*mx* + *m* + 1 = 0 has real roots is

(1) 1/5

(2) 2/5

**(3) 3/5 **

(4) 4/5

**Ans: (3)**

*Solution*

Tags : Introduction to Probability Theory | Mathematics , 11th Mathematics : UNIT 12 : Introduction to Probability Theory

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11th Mathematics : UNIT 12 : Introduction to Probability Theory : Exercise 12.5: Choose the correct answer | Introduction to Probability Theory | Mathematics

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