11th Business Maths Monthly Test - 1 ( Descriptive Statistics and Probability )

MABS Institution

11th Business Maths Monthly Test - 1 ( Descriptive Statistics and Probability )-Aug 2020

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

The median of 10,14,11,9,8,12,6 is

The first quartile is also known as

median.
lower quartile.
mode.
third decile

The harmonic mean of the numbers 2,3,4 is

\(\frac { 12 }{ 13 } \)
2
\(\frac { 36 }{ 13 } \)
\(\frac { 13 }{ 36 } \)

If two events A and B are dependent then the conditional probability of P(B/A) is

\(P(A)P(B/A)\)
\(\frac { P(A\cup B) }{ P(B) } \)
\(\frac { P(A\cap B) }{ P(A) } \)
\(P(A)P(A/B)\)

Let a sample space of an experiment be S = { E₁,E₂,....., En} Then \(\sum _{ i=1 }^{ n }{ P({ E }_{ t }) } \) is equal to

0
1
\(\frac { 1 }{ 2 } \)
\(\frac { 1 }{ 3 } \)

The two events A and B are mutually exclusive if

\(P\left( A\cap B \right) =0\)
\(P\left( A\cap B \right) =1\)
\(P\left( A\cup B \right) =0\)
\(P\left( AUB \right) =1\)

When calculating the average growth of economy, the correct mean to use is?

Weighted mean
Arithmetic mean
Geometric mean
Harmonic mean

When an observation in the data is zero, then its geometric mean is

Negative
Positive
Zero
Cannot be calculated

The events A and B are independent if

\(P\left( A\cap B \right) =0\)
\(P\left( A\cap B \right) =P(A)\times P(B)\)
\(P\left( A\cup B \right) =P(A)+P(B)\)
\(P\left( A\cup B \right) =P(A)\times P(B)\)

If the outcome of one event does not influence another event then the two events are

Mutually exclusive
Dependent
Not disjoint
Independent

Part - B

Generic 2 - Answer All Question

Find D₂ and D₆ for the following series 22, 4, 2, 12, 16, 6, 10, 18, 14, 20, 8

Let P(A)=\(\frac{3}{5}\) and P(B)=\(\frac{1}{5}\) . Find P(A∩B) if A and B are independent events.

An investor buys Rs. 1,500 worth of shares in a company each month. During the first four months he bought the shares at a price of Rs. 10, 15, 20 and 30 per share. What is the average price paid for the shares bought during these four months? Verify your result.

A family has two children. What is the probability that both the children are girls given that at least one of them is a girl?

From a pack of 52 cards, two cards are drawn at random. Find the probability that one is a king and the other is a queen.
An unbiased die is thrown. If A is the event ‘the number appearing is a multiple of 3’ and B be the event ‘the number appearing is even’ number then find whether A and B are independent?

A person purchases tomatoes from each of the 4 places at the rate of 1kg., 2kg., 3kg., and 4kg. per rupee respectively .On the average, how many kilograms has he purchased per rupee?

Find the first quartile and third quartile for the given observations
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22

A die is thrown twice and the sum of the number appearing is observed to be 6. What is the conditional probability that the number 4 has appeared at least once?

A committee of two persons is formed from 3 men and 2 women. What is the probability that the committee will have
(i) No woman (ii) One man (iii) No man

Part - C

Generic 3 - Answer All Question

Find the probability of drawing a queen, a king and a knave (Jack) in that order from a pack of cards in three consecutive draws, the card drawn not being replaced.

Find the harmonic mean of 6, 14, 21, 30

Calculate the Mean Deviation about mean and its coefficient of the income groups of five, given below

Income Rs 4000 4200 4400 4600 4800

Find the mean deviation about the mean of the following observations 2, 3, 5, 6, 9, 10, 12, 17, 20, 26 and n = 10

A bg contains (2n+1) coins. It is known that n of these coins have a head on both sides whereas the rest of the coins are fair. A coin is picked up at random from the bag and is tossed. If the probability that the toss results in a head is \(\frac { 31 }{ 42 } \) , determine the value of n.

Calculate the value of Q₁, Q₃, D₆ and P₅₀ from the following data

Roll No 1 2 3 4 5 6 7

Marks 20 28 40 12 30 15 50
A fair die is rolled. A = {1, 3, 5} B = {2, 3} and C = {2, 3, 4, 5}. Find (i) P(A/B) and P(B/A) (ii) P(A/C) and p(C/A).

A die is thrown. Find the probability of getting
(i) a prime number
(ii) a number greater than or equal to 3

Calculate the harmonic mean for:

Size 6 7 8 9 10 11

Frequency 4 6 9 5 2 8

Calculate the geometric mean of the data given below giving the number of families and the income per head of different classes of people in a village of Kancheepuram District.

Class of people No. of Families Income per head in 1990 (Rs)

Landlords 1 1000

Cultivators 50 80

Landless labourers 25 40

Money- lenders 2 750

School teachers 3 100

Shop-keepers 4 150

Carpenters 3 120

Weavers 5 60

Part - D

Generic 5 - Answer All Question

There are 1000 students in a school out of which 450 are girls. It is known that out of 450, 20% of the girls studying in class XI. A student is randomly selected from 1000 students. What is the probability that the selected student is from class XI given that the selected student is a girl?

A box contains 4 red, 6 green balls. Two balls are picked out one by one at random without replacement. What is the probability that the second is green given that the first one is green?

In a screw factory machines A, B, C manufacture respectively 30%, 40% and 30% of the total output of these 2%, 4% and 6% percent are defective screws. A screws is drawn at random from the product and is found to be defective. What is the probability that it was manufactured by Machine C?

Three events A, B and C have probabilities \(\frac { 2 }{ 5 } ,\frac { 1 }{ 3 } \) and \(\frac { 1 }{ 2 } \) respectively. Given that \(P(A\cap C)=\frac { 1 }{ 5 } \) and \(P(B\cap C)=\frac { 1 }{ 4 } ,\)find P(C/B) and \(P(\bar { A } \cap \bar { C } )\)

In a Shooting test, the probabilities of hitting the target are \(\frac { 1 }{ 2 } \) for A, \(\frac { 2 }{ 3 } \) for B and \(\frac { 3 }{ 4 } \) for C. If all of them fire at the same target, calculate the probabilities that only one of them hit the target.

Find out the coefficient of mean deviation about median in the following series.

Age in years 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80

No. of persons 20 25 32 40 42 35 10 8

Calculations have to be made correct to two places of decimals.
There are 3 boxes containing respectively 1 white, 2 red, 3 black balls; 2 white, 3 red and 1 black ball; 2 white, 1 red, 3 black balls. A box is chosen t random and from it 2 balls are drawn at random. The 2 balls are 1 red and 1 white. What is the probability that they come from the second box?

The first of three urns contains 7 White and 10 Black balls, the second contains 5 White and 12 Black balls and third contains 17 White balls and no Black ball. A person chooses an urn at random and draws a ball from it. And the ball is found to be White. Find the probabilities that the ball comes from
(i) the first urn
(ii) the second urn
(iii) the third urn

Two identical boxes containing respectively 4 white and 3 red balls, 3 white and 7 red balls. A box is chosen at random and a ball is drawn from it. Find the probability that the ball is white. If the ball is white. If the ball is white, what is the probability that it is from first box?

Find D₆,D₈,P₇ and P₂₀ for the data 57, 58, 61, 42, 38, 65, 72, 66.

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Class of people	No. of Families	Income per head in 1990 (Rs)
Landlords	1	1000
Cultivators	50	80
Landless labourers	25	40
Money- lenders	2	750
School teachers	3	100
Shop-keepers	4	150
Carpenters	3	120
Weavers	5	60

Age in years	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80
No. of persons	20	25	32	40	42	35	10	8

Roll No	1	2	3	4	5	6	7
Marks	20	28	40	12	30	15	50

Size	6	7	8	9	10	11
Frequency	4	6	9	5	2	8

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11th Business Maths Monthly Test - 1 ( Descriptive Statistics and Probability )

MABS Institution

11th Business Maths Monthly Test - 1 ( Descriptive Statistics and Probability )-Aug 2020

Part - A

Multiple Choice Question - Answer All Question

The median of 10,14,11,9,8,12,6 is

The first quartile is also known as

The harmonic mean of the numbers 2,3,4 is

If two events A and B are dependent then the conditional probability of P(B/A) is

Let a sample space of an experiment be S = { E1,E2,....., En} Then \(\sum _{ i=1 }^{ n }{ P({ E }_{ t }) } \) is equal to

The two events A and B are mutually exclusive if

When calculating the average growth of economy, the correct mean to use is?

When an observation in the data is zero, then its geometric mean is

The events A and B are independent if

If the outcome of one event does not influence another event then the two events are

Part - B

Generic 2 - Answer All Question

Find D2 and D6 for the following series 22, 4, 2, 12, 16, 6, 10, 18, 14, 20, 8

Let P(A)=\(\frac{3}{5}\) and P(B)=\(\frac{1}{5}\) . Find P(A∩B) if A and B are independent events.

An investor buys Rs. 1,500 worth of shares in a company each month. During the first four months he bought the shares at a price of Rs. 10, 15, 20 and 30 per share. What is the average price paid for the shares bought during these four months? Verify your result.

A family has two children. What is the probability that both the children are girls given that at least one of them is a girl?

From a pack of 52 cards, two cards are drawn at random. Find the probability that one is a king and the other is a queen.

An unbiased die is thrown. If A is the event ‘the number appearing is a multiple of 3’ and B be the event ‘the number appearing is even’ number then find whether A and B are independent?

A person purchases tomatoes from each of the 4 places at the rate of 1kg., 2kg., 3kg., and 4kg. per rupee respectively .On the average, how many kilograms has he purchased per rupee?

Find the first quartile and third quartile for the given observations 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22

A die is thrown twice and the sum of the number appearing is observed to be 6. What is the conditional probability that the number 4 has appeared at least once?

A committee of two persons is formed from 3 men and 2 women. What is the probability that the committee will have (i) No woman (ii) One man (iii) No man

Part - C

Generic 3 - Answer All Question

Find the probability of drawing a queen, a king and a knave (Jack) in that order from a pack of cards in three consecutive draws, the card drawn not being replaced.

Find the harmonic mean of 6, 14, 21, 30

Calculate the Mean Deviation about mean and its coefficient of the income groups of five, given below Income Rs 4000 4200 4400 4600 4800

Find the mean deviation about the mean of the following observations 2, 3, 5, 6, 9, 10, 12, 17, 20, 26 and n = 10

A bg contains (2n+1) coins. It is known that n of these coins have a head on both sides whereas the rest of the coins are fair. A coin is picked up at random from the bag and is tossed. If the probability that the toss results in a head is \(\frac { 31 }{ 42 } \) , determine the value of n.

Calculate the value of Q1, Q3, D6 and P50 from the following data Roll No 1 2 3 4 5 6 7 Marks 20 28 40 12 30 15 50

A fair die is rolled. A = {1, 3, 5} B = {2, 3} and C = {2, 3, 4, 5}. Find (i) P(A/B) and P(B/A) (ii) P(A/C) and p(C/A).

A die is thrown. Find the probability of getting (i) a prime number (ii) a number greater than or equal to 3

Calculate the harmonic mean for: Size 6 7 8 9 10 11 Frequency 4 6 9 5 2 8

Part - D

Generic 5 - Answer All Question

There are 1000 students in a school out of which 450 are girls. It is known that out of 450, 20% of the girls studying in class XI. A student is randomly selected from 1000 students. What is the probability that the selected student is from class XI given that the selected student is a girl?

A box contains 4 red, 6 green balls. Two balls are picked out one by one at random without replacement. What is the probability that the second is green given that the first one is green?

In a screw factory machines A, B, C manufacture respectively 30%, 40% and 30% of the total output of these 2%, 4% and 6% percent are defective screws. A screws is drawn at random from the product and is found to be defective. What is the probability that it was manufactured by Machine C?

Three events A, B and C have probabilities \(\frac { 2 }{ 5 } ,\frac { 1 }{ 3 } \) and \(\frac { 1 }{ 2 } \) respectively. Given that \(P(A\cap C)=\frac { 1 }{ 5 } \) and \(P(B\cap C)=\frac { 1 }{ 4 } ,\)find P(C/B) and \(P(\bar { A } \cap \bar { C } )\)

In a Shooting test, the probabilities of hitting the target are \(\frac { 1 }{ 2 } \) for A, \(\frac { 2 }{ 3 } \) for B and \(\frac { 3 }{ 4 } \) for C. If all of them fire at the same target, calculate the probabilities that only one of them hit the target.

Find out the coefficient of mean deviation about median in the following series. Age in years 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 No. of persons 20 25 32 40 42 35 10 8 Calculations have to be made correct to two places of decimals.

There are 3 boxes containing respectively 1 white, 2 red, 3 black balls; 2 white, 3 red and 1 black ball; 2 white, 1 red, 3 black balls. A box is chosen t random and from it 2 balls are drawn at random. The 2 balls are 1 red and 1 white. What is the probability that they come from the second box?

Two identical boxes containing respectively 4 white and 3 red balls, 3 white and 7 red balls. A box is chosen at random and a ball is drawn from it. Find the probability that the ball is white. If the ball is white. If the ball is white, what is the probability that it is from first box?

Find D6,D8,P7 and P20 for the data 57, 58, 61, 42, 38, 65, 72, 66.

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Let a sample space of an experiment be S = { E₁,E₂,....., En} Then \(\sum _{ i=1 }^{ n }{ P({ E }_{ t }) } \) is equal to

Find D₂ and D₆ for the following series 22, 4, 2, 12, 16, 6, 10, 18, 14, 20, 8

Find the first quartile and third quartile for the given observations
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22

A committee of two persons is formed from 3 men and 2 women. What is the probability that the committee will have
(i) No woman (ii) One man (iii) No man

Calculate the Mean Deviation about mean and its coefficient of the income groups of five, given below

Income Rs 4000 4200 4400 4600 4800

Calculate the value of Q₁, Q₃, D₆ and P₅₀ from the following data

Roll No 1 2 3 4 5 6 7

Marks 20 28 40 12 30 15 50

A die is thrown. Find the probability of getting
(i) a prime number
(ii) a number greater than or equal to 3

Calculate the harmonic mean for:

Size 6 7 8 9 10 11

Frequency 4 6 9 5 2 8

Find out the coefficient of mean deviation about median in the following series.

Age in years 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80

No. of persons 20 25 32 40 42 35 10 8

Calculations have to be made correct to two places of decimals.

Find D₆,D₈,P₇ and P₂₀ for the data 57, 58, 61, 42, 38, 65, 72, 66.