11th Maths Monthly Test -3 ( Introduction to probability theory )

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test -3 ( Introduction to probability theory )-Aug 2020

Time : 2.00 Hours

Part - A

Generic 2 - Answer All Question

There are two identical urns containing respectively 6 black and 4 red balls, 2 black and 2 red balls. An urn is chosen at random and a ball is drawn from it.
(i) find the probability that the ball is black
(ii) if the ball is black, what is the probability that it is from the first urn?

An experiment has the four possible mutually exclusive and exhaustive outcomes A, B, C, and D. Check whether the following assignments of probability are permissible
P(A) = 0.22 , P(B) = 0.38 , P(C) = 0. 16, P (D) = 0.34

Five mangoes and 4 apples are in a box. If two fruits are chosen at random, find the probability that (i) one is a mango and the other is an apple (ii) both are of the same variety

Suppose P(B) = \(\frac {2 }{ 5 } \) Express the odds that the event B occurs

If A' is complementary event of A.P,.T P[A'}=1-P[A]

If A and B are two independent events such that, P(A)=0.4 and P\((A\cup B)\)=0.9. Find P(B).

If an experiment has exactly the three possible mutually exclusive outcomes A, B, and C, check in each case whether the assignment of probability is permissible
\(P(A)=\frac { 4 }{ 7 } ,P(B)=\frac { 1 }{ 7 } ,P(C)=\frac { 2 }{ 7 } \)

(i) The odds that the event A occurs is 5 to 7, find P(A).,

(ii) Suppose P(B) = \(\frac{2}{5}\). Express the odds that the event B occurs.

If A and B are 2 events such that P{AUB} =.7,P{AnB] =.2 & P{B} =.5 S.T A and B are independent

If an experiment has exactly the three possible mutually exclusive outcomes A, B, and C, check in each case whether the assignment of probability is permissible
P(A)=0.421, P(B)=0.527 P(C)=0.042

Given that P(A) =0.52, P(B)=0.43, and P(A∩B)=0.24, find
P\(\left( \overline { A } \cap \overline { B } \right) \)

The probability that student selected at random from a class will pass in Mathematics is \(\frac { 2 }{ 3 } \) and the probability that he passes in Mathematics and English is \(\frac { 1 }{ 3 } \). What is the probability that he will pass in English if it is known that he has passed in Mathematics?

Given that P(A) =0.52, P(B)=0.43, and P(A∩B)=0.24, find
P(A∪B)

Nine coins are tossed once, find the probability to get at least two heads

Part - B

Generic 3 - Answer All Question

A die is rolled. If the outcome is an even number, what is the probability that it is a prime number?

A fair dice is rolled. Consider the following events 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\(\cap \)B/C)

The probability that a person will get an electric contract \(\frac { 2 }{ 3 } \) and the probability that he will not get plumbing contract is \(\frac { 4 }{ 7 } \). If the probability of getting atleast one contract is \(\frac { 2 }{ 3 } \). What is the probability tht he will get both?

A town has 2 fire engines operating independently. The probability that a fire engine is available when needed is 0.96.
(i) What is the probability that a fire engine is available when needed?
(ii) What is the probability that neither is available when needed?

A bag contains 10 white and 15 black balls. 2 balls are drawn in succession without replacement. What is the probability that first is white and second is black?

The probability of an event A occurring is 0.5 and B occurring is 0.3. If A and B are mutually exclusive events, then find the probability of
(i) \(P(A\cup B)\)
(ii) \(P(A\cap \bar { B } )\)
(iii) \(P(\bar { A } \cap B)\)

A die is thrown 3 times. Events A and B are defined as follows.
A: getting 4 on third die
B: getting 6 on the first and 5 on the second throw. Find the probability of A given that B has already occurred.

A firm manufactures PVC pipes in three plants viz, X, Y, and Z. The daily production volumes from the three firms X, Y and Z are respectively 2000 units, 3000 units, and 5000 units. It is known from the past experience that 3% of the output from plant X, 4% from plant Y and 2% from plant Z are defective. A pipe is selected at random from a day’s total production,
(i) find the probability that the selected pipe is a defective one.
(ii) if the selected pipe is a defective, then what is the probability that it was produced by plant Y?

Suppose a fair die is rolled. Find the probability of getting
(i) an even number (ii) multiple of three

A die is thrown twice. Let A be the event, ‘First die shows 5’ and B be the event 'second die shows 5’. Find \(P(A\cup B)\) .

The probability that a car being filled with petrol will also need an oil change is 0.30; the probability that it needs a new oil filter is 0.40; and the probability that both the oil and filter need changing is 0.15.
(i) If the oil had to be changed, what is the probability that a new oil filter is needed?
(ii) If a new oil filter is needed, what is the probability that the oil has to be changed

A die is rolled. If it shows an odd number, then find the probability of getting 5.

Let the matrix M=\(\left[ \begin{matrix} x & y \\ z & 1 \end{matrix} \right] \), If x,y and z are chosen at random from the set {1, 2,3, } and repetition is allowed (i.e., x=y=z ), what is the probability that the given matrix M is a singular matrix?

One card is drawn from a well shuffled pack of 52 cards. If E is the event, "the card drawn is a king or queen" and F is the event "the card drawn is a queen or an ace", then find P(E/F).

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11th Maths Monthly Test -3 ( Introduction to probability theory )

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test -3 ( Introduction to probability theory )-Aug 2020

Part - A

Generic 2 - Answer All Question

There are two identical urns containing respectively 6 black and 4 red balls, 2 black and 2 red balls. An urn is chosen at random and a ball is drawn from it. (i) find the probability that the ball is black (ii) if the ball is black, what is the probability that it is from the first urn?

An experiment has the four possible mutually exclusive and exhaustive outcomes A, B, C, and D. Check whether the following assignments of probability are permissible P(A) = 0.22 , P(B) = 0.38 , P(C) = 0. 16, P (D) = 0.34

Five mangoes and 4 apples are in a box. If two fruits are chosen at random, find the probability that (i) one is a mango and the other is an apple (ii) both are of the same variety

Suppose P(B) = \(\frac {2 }{ 5 } \) Express the odds that the event B occurs

If A' is complementary event of A.P,.T P[A'}=1-P[A]

If A and B are two independent events such that, P(A)=0.4 and P\((A\cup B)\)=0.9. Find P(B).

If an experiment has exactly the three possible mutually exclusive outcomes A, B, and C, check in each case whether the assignment of probability is permissible \(P(A)=\frac { 4 }{ 7 } ,P(B)=\frac { 1 }{ 7 } ,P(C)=\frac { 2 }{ 7 } \)

(i) The odds that the event A occurs is 5 to 7, find P(A)., (ii) Suppose P(B) = \(\frac{2}{5}\). Express the odds that the event B occurs.

If A and B are 2 events such that P{AUB} =.7,P{AnB] =.2 & P{B} =.5 S.T A and B are independent

If an experiment has exactly the three possible mutually exclusive outcomes A, B, and C, check in each case whether the assignment of probability is permissible P(A)=0.421, P(B)=0.527 P(C)=0.042

Given that P(A) =0.52, P(B)=0.43, and P(A∩B)=0.24, find P\(\left( \overline { A } \cap \overline { B } \right) \)

Given that P(A) =0.52, P(B)=0.43, and P(A∩B)=0.24, find P(A∪B)

Nine coins are tossed once, find the probability to get at least two heads

Part - B

Generic 3 - Answer All Question

A die is rolled. If the outcome is an even number, what is the probability that it is a prime number?

A fair dice is rolled. Consider the following events 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\(\cap \)B/C)

The probability that a person will get an electric contract \(\frac { 2 }{ 3 } \) and the probability that he will not get plumbing contract is \(\frac { 4 }{ 7 } \). If the probability of getting atleast one contract is \(\frac { 2 }{ 3 } \). What is the probability tht he will get both?

A town has 2 fire engines operating independently. The probability that a fire engine is available when needed is 0.96. (i) What is the probability that a fire engine is available when needed? (ii) What is the probability that neither is available when needed?

A bag contains 10 white and 15 black balls. 2 balls are drawn in succession without replacement. What is the probability that first is white and second is black?

The probability of an event A occurring is 0.5 and B occurring is 0.3. If A and B are mutually exclusive events, then find the probability of (i) \(P(A\cup B)\) (ii) \(P(A\cap \bar { B } )\) (iii) \(P(\bar { A } \cap B)\)

A die is thrown 3 times. Events A and B are defined as follows. A: getting 4 on third die B: getting 6 on the first and 5 on the second throw. Find the probability of A given that B has already occurred.

Suppose a fair die is rolled. Find the probability of getting (i) an even number (ii) multiple of three

A die is thrown twice. Let A be the event, ‘First die shows 5’ and B be the event 'second die shows 5’. Find \(P(A\cup B)\) .

A die is rolled. If it shows an odd number, then find the probability of getting 5.

Let the matrix M=\(\left[ \begin{matrix} x & y \\ z & 1 \end{matrix} \right] \), If x,y and z are chosen at random from the set {1, 2,3, } and repetition is allowed (i.e., x=y=z ), what is the probability that the given matrix M is a singular matrix?

One card is drawn from a well shuffled pack of 52 cards. If E is the event, "the card drawn is a king or queen" and F is the event "the card drawn is a queen or an ace", then find P(E/F).

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Tamilnadu Stateboardszs - Class

There are two identical urns containing respectively 6 black and 4 red balls, 2 black and 2 red balls. An urn is chosen at random and a ball is drawn from it.
(i) find the probability that the ball is black
(ii) if the ball is black, what is the probability that it is from the first urn?

An experiment has the four possible mutually exclusive and exhaustive outcomes A, B, C, and D. Check whether the following assignments of probability are permissible
P(A) = 0.22 , P(B) = 0.38 , P(C) = 0. 16, P (D) = 0.34

If an experiment has exactly the three possible mutually exclusive outcomes A, B, and C, check in each case whether the assignment of probability is permissible
\(P(A)=\frac { 4 }{ 7 } ,P(B)=\frac { 1 }{ 7 } ,P(C)=\frac { 2 }{ 7 } \)

(i) The odds that the event A occurs is 5 to 7, find P(A).,

(ii) Suppose P(B) = \(\frac{2}{5}\). Express the odds that the event B occurs.

If an experiment has exactly the three possible mutually exclusive outcomes A, B, and C, check in each case whether the assignment of probability is permissible
P(A)=0.421, P(B)=0.527 P(C)=0.042

Given that P(A) =0.52, P(B)=0.43, and P(A∩B)=0.24, find
P\(\left( \overline { A } \cap \overline { B } \right) \)

Given that P(A) =0.52, P(B)=0.43, and P(A∩B)=0.24, find
P(A∪B)

A town has 2 fire engines operating independently. The probability that a fire engine is available when needed is 0.96.
(i) What is the probability that a fire engine is available when needed?
(ii) What is the probability that neither is available when needed?

The probability of an event A occurring is 0.5 and B occurring is 0.3. If A and B are mutually exclusive events, then find the probability of
(i) \(P(A\cup B)\)
(ii) \(P(A\cap \bar { B } )\)
(iii) \(P(\bar { A } \cap B)\)

A die is thrown 3 times. Events A and B are defined as follows.
A: getting 4 on third die
B: getting 6 on the first and 5 on the second throw. Find the probability of A given that B has already occurred.

Suppose a fair die is rolled. Find the probability of getting
(i) an even number (ii) multiple of three