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Test: Probability And Expected Value By Mathematical Expectation- 6

40 Questions MCQ Test Quantitative Aptitude for CA CPT | Test: Probability And Expected Value By Mathematical Expectation- 6

Description

Attempt Test: Probability And Expected Value By Mathematical Expectation- 6 | 40 questions in 40 minutes | Mock test for CA Foundation preparation | Free important questions MCQ to study Quantitative Aptitude for CA CPT for CA Foundation Exam | Download free PDF with solutions

QUESTION: 1

The probability of winning of a person is 6/11 and at a result he gets Rs.77/= .The expectation of this person is

A.
Rs.35/=
B.
Rs.42/=
C.
Rs.58/=
D.
none

Solution:

QUESTION: 2

A family has 2 children. The probability that both of them are boys if it is known that one of them is a boy

A.
1
B.
1/3
C.
3/4
D.
none

Solution:

QUESTION: 3

The Probability of the occurrence of a no. greater then 2 in a throw of a die if it is known that only even nos. can occur is

A.
1/3
B.
1/2
C.
2/3
D.
none

Solution:

Total events are 6
Possibility of Greater than 2 is 4 i.e. 3, 4, 5, 6
Hence, Probability of the occurrence of a no. greater then 2 will be 4/6

=2/3

QUESTION: 4

A player has 7 cards in hand of which 5 are red and of these five 2 are kings. A card is drawn at random. The probability that it is a king, it being known that it is red is

A.
2/5
B.
3/5
C.
4/5
D.
none

Solution:

QUESTION: 5

In a class 40 % students read Mathematics, 25 % Biology and 15 % both Mathematics and Biology. One student is select at random. The probability that he reads Mathematics if it is known that he reads Biology is

A.
2/5
B.
3/5
C.
4/5
D.
none

Solution:

QUESTION: 6

In a class 40 % students read Mathematics, 25 % Biology and 15 % both Mathematics and Biology. One student is select at random.The probability that he reads Biology if he reads Mathematics

A.
7/8
B.
1/8
C.
3/8
D.
none

Solution:

QUESTION: 7

Probability of throwing an odd no with an ordinary six faced die is

A.
1/2
B.
1
C.
–1/2
D.
0

Solution:

QUESTION: 8

For a certain event A ,P (A) is equal to

A.
1
B.
0
C.
–1
D.
none

Solution:

QUESTION: 9

When none of the outcomes is favourable to the event then the event is said to be

A.
certain
B.
sample
C.
impossible
D.
none

Solution:

QUESTION: 10

The probability of selecting sample of size 'n' out of a population of size N by simple random sampling with replacement is:

A.
1/N
B.
1/Nⁿ
C.
1/^Nc_n
D.

Solution:

QUESTION: 11

If P(A) = 0.45, P(B) = 0.35 and P(A & B) = 0.25, then P(A/B)=?

A.
1.4
B.
1.8
C.
0.714
D.
0.556

Solution:

QUESTION: 12

Find the probability of drawing a spade on each of two consecutive draws from a well shuffled pack of cards, without replacement

A.
2/15
B.
1/17
C.
4/51
D.
5/51

Solution:

in a pack of card there are total 52 Cards

Spade cards are 13

Probability that two consecutive cards drawn from a well shuffled pack of cards are spade = ¹³C₂ / ⁵²C₂

= 13 * 12 / 52 * 51

= 12 / 4 * 51

= 3/51

= 1/17

other ways

probability of Choosing 1st card as spade = (13/52) = 1/4

Probability of choosing 2nd spade card = 12/51 = 4/17

(1/4)(4/17) = 1/17

QUESTION: 13

If a pair of dice is thrown then the probability that the sum of the digit is neither 7 nor 11 is _____.

A.
1/6
B.
1/18
C.
2/9
D.
7/9

Solution:

QUESTION: 14

A player tosses 3 fair coins. He wins Rs.5 if three appear, Rs.3 if two heads appear, Rs.1 if one head occurs. On the other hand, he losses Rs.15 if 3 tails occur. Find expected gain of the player.

A.
0.15
B.
0.25
C.
0.35
D.
0.45

Solution:

QUESTION: 15

The probability of a cricket term winning match at Kanpur is 2/5 and hosing match at Delhi is 1/7 what is the Probability of the term winning atleast one match?

A.
3/35
B.
32/35
C.
18/35
D.
17/35

Solution:

QUESTION: 16

Two coins are tossed simultaneously. Find the probability of getting exactly one head.

A.
3/4
B.
2/3
C.
1/4
D.
1/2

Solution:

QUESTION: 17

For any two events A₁, A₂ letP(A₁) = 2/3,P(A₂) = 3/8 and P(A₁ ∩ A₂) =1/4 then A₁, A₂are:

A.
Mutually exclusive but not independent events
B.
Mutually exclusive and independent events
C.
Independent but not mutually exclusive
D.
None of these

Solution:

QUESTION: 18

Find the expected value of the following probability distribution

1/20

A.
20.5
B.
21.5
C.
22.5
D.
24.5

Solution:

QUESTION: 19

The odds against A solving a certain problem are 4 to 3 and the odds in favour of B solving the same problem are 7 to 5. What is the probability that the problem will be solved if they both try?

A.
15/21
B.
16/21
C.
17/21
D.
13/21

Solution:

QUESTION: 20

A box contains 2 red, 3 green and 2 blue balls. Two bails are drawn at random. What is the probability that none of the balls drawn is blue?

A.
10/21
B.
11/21
C.
2/7
D.
5/7

Solution:

QUESTION: 21

The odds that a book will be favourable received by 3 independent received by 3 independent reviewers are 5 to 2, 4 to 3 and 4 to 4 respectively. What is the probability that out of 3 reviewers a majority will be favourable?

A.
209/343
B.
209/434
C.
209/443
D.
209/350

Solution:

QUESTION: 22

An urn contains 2 red and 1 green balls. nother urn contains 2 red and 2 green balls. An urn was selected at random and then a ball was drawn from it. If it was found to be red then the probability that it has been drawn from urn one is ______.

A.
4/7
B.
3/7
C.
2/3
D.
7/12

Solution:

QUESTION: 23

Find the expected value of the following probability distribution

A.
20.5
B.
21.5
C.
22.5
D.
24.5

Solution:

QUESTION: 24

A bag contains 6 red balls and some blue balls. If the probability of drawing a blue ball form the bag is twice that of a red ball, find the number of blue balls in the bag

A.
10
B.
12
C.
14
D.
16

Solution:

QUESTION: 25

A company employed 7 CA's, 6 MBA's and 3 Engineer's. In how many ways the company can form a committe, if the committee has two members of each type.

A.
900
B.
1,000
C.
787
D.
945

Solution:

QUESTION: 26

In a packet of 500 pens, 50 are found to be defective. A pen is selected at random. Find the probability that it is non defective.

A.
8/9
B.
7/8
C.
9/10
D.
2/3

Solution:

QUESTION: 27

A bag contains 5 Red balls, 4 Blue Balls and 'm' Green Balls. If the random probability of picking two green balls is 1/7. What is the no. of green Balls (m).

A.
5
B.
7
C.
6
D.
None of the above.

Solution:

QUESTION: 28

Four married couples have gathered in a room. Two persons are selected at random amongst them, find the probability that selected persons are a gentleman and a lady but not a Couple.

A.
1/7
B.
3/7
C.
1/8
D.
3/8

Solution:

QUESTION: 29

The odds against A solving a certain problem are 4 to 3 and the odds in favour of B solving the same problem are 7 to 5. What is the probability that the problem will be solved if they both try?

A.
15/21
B.
16/21
C.
17/21
D.
13/21

Solution:

QUESTION: 30

One Card is drawn from pack of 52, what is the probability that it is a king or a queen?

A.
11/13
B.
2/13
C.
1/13
D.
None of these

Solution:

QUESTION: 31

A player tosses two fair coins, he wins Rs.5 of 2 head appear, Rs.2 if one head appears and Rs.1 if no head occurs. Find his expected amount of winning.

A.
2.5
B.
3.5
C.
4.5
D.
5.5

Solution:

QUESTION: 32

Arun & Tarun appear for an interview for two vacancies. The probability of Arun's selection is 1/3 and that of Tarun's selection is 1/5. Find the probability that only one of them will be selected.

A.
2/5
B.
4/5
C.
6/5
D.
8/5

Solution:

QUESTION: 33

If 15 persons are to be seated around 2 round tables, one occupying 8 persons and another 7 persons.Find the number of ways in which they can be seated.

A.
B.
C.
7!.8!
D.
2.¹⁵C₇6!7!

Solution:

QUESTION: 34

The probability of Girl getting scholarship is 0.6 and the same probability for Boy is 0.8. Find the probability that at least one of the categories getiing scholarship.

A.
0.32
B.
0.44
C.
0.92
D.
None of the above.

Solution:

QUESTION: 35

A coin is tossed 5 times, what is the probability that exactly 3 heads will occur.

A.
5/16
B.
1/32
C.
5/36
D.
3/32

Solution:

QUESTION: 36

Two dice are thrown together. Find the probability of getting a multiple of 2 on one dice and multiple of 3 on the other.

A.
2/3
B.
5/18
C.
1/13
D.
None of the above.

Solution:

Two dice are thrown simultaneously

S={(1,1),(1,2),(1,3),(1,4),(1,5), (1,6)

(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)

(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)

(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)

(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)

(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)}

n(s)=36

Event A : getting multiple of 2 on one die and multiple of 3 on other die
A={(2,3)(2,6)(4,3)(4,6) (6,3)(6,6)(6,2)(6,4)(3,2)(3,6)}
n(A)=10
p(A)=n(A)/n(s)
=10/36
=5/18