11th Maths Monthly Test - 1 ( Introduction to probability theory )

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test - 1 ( Introduction to probability theory )-Aug 2020

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

If P(A) = 0.4, P(B) = 0.3 and P(AUB) = 0.5, then \(P(\bar { B } \cap A)\)

\(\frac { 2 }{ 3 } \)
\(\frac { 1 }{ 2 } \)
\(\frac { 3 }{ 10 } \)
\(\frac { 1 }{ 5 } \)

If A and B are two events such that P(A)= 0.4, P(B)= 0.8, and P(B/A)=0.6,then \(P(\overline{A}\cap B )\)is

0.96
0.24
0.56
0.66

If A and B are two events such that P(A) = \(\frac { 4 }{ 5 } \) and \(P(A\cap B)=\frac { 7 }{ 10 } \) then P(B/A) =

\(\frac { 1 }{ 10 } \)
\(\frac { 1 }{ 8 } \)
\(\frac { 7 }{ 8 } \)
\(\frac { 17 }{ 20 } \)

Let A and B be two events such that P(A) = 0.6, P(B) = 0.2 and P(A/B) = 0.5, Then P(\(\bar { A } /\bar { B } \)) is

\(\frac { 1 }{ 10 } \)
\(\frac { 3 }{ 10 } \)
\(\frac { 3 }{ 8 } \)
\(\frac { 6 }{ 7 } \)

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?

1:12
12:1
13:1
1:13

Out of 30 consecutive integers, 2 are chosen at random. The probability that their sum is odd is

\(\frac { 14 }{ 29 } \)
\(\frac { 16 }{ 29 } \)
\(\frac { 15 }{ 29 } \)
\(\frac { 10 }{ 29 } \)

Two dice are thrown. It is known that the sum of the numbers on the dice was less than 6, the probability of getting a sum 3 is

\(\frac { 1 }{ 18 } \)
\(\frac { 5 }{ 18 } \)
\(\frac { 1 }{ 5 } \)
\(\frac { 2 }{ 5 } \)

The probability that in a year of 22^nd century, chosen at random there will be 53 Sundays is

\(\frac { 3 }{ 28 } \)
\(\frac { 2 }{ 28 } \)
\(\frac { 7 }{ 28 } \)
\(\frac { 5 }{ 28 } \)

A letter is taken at random from the letters of the word ‘ASSISTANT’ and another letter is taken at random from the letters of the word ‘STATISTICS’. The probability that the selected letters are the same is

\({7\over 45}\)
\({17\over 90}\)
\({29\over 90}\)
\({19\over 90}\)

Three integers are chosen at random from the first 20 integers. The probability that their product is even is

\(\frac { 2 }{ 19 } \)
\(\frac { 3 }{ 19 } \)
\(\frac { 17 }{ 19 } \)
\(\frac { 4 }{ 19 } \)

Part - B

Generic 2 - Answer All Question

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

Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.

Find the probability of getting the number 7, when a usual die is rolled

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
\(P(A)=0.3,P(B)=0.9,P(C)=-0.2\)
A bag contains 7 red and 4 black balls, 3 balls are drawn at random. Find the probability that (i) all are red (ii) one red and 2 black

An integer is chosen at random from the first 100 positive integers. What is the probability that the integer chosen is a prime or multiple of 8?

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

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

If two coins are tossed simultaneously, then find the probability of getting
(i) one head and one tail (ii) at most two tails

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

Part - C

Generic 3 - Answer All Question

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

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

If A and B are mutually exclusive events P(A)=\(\frac{3}{8}\) and P(B)=\(\frac{1}{8}\) , then find
(i) P(\(\bar { A } \))
(ii) \(P(A\cup B)\)
(iii) \(P(\bar { A } \cap B)\)
(iv) \(P(\bar { A } \cup \bar { B } )\)

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?

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

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 problem in Mathematics is given to three students whose chances of solving A problem in Mathematics is given to three students whose chances of solving \(\frac { 1 }{ 3 } ,\frac { 1 }{ 4 } \) and \(\frac { 1 }{ 5 } \) (i) What is the probability that the problem is solved? (ii) What is the probability that exactly one of them will solve it?

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

If for two events A and B, P(A)=\(\frac{3}{4}\), P(B)=\(\frac{2}{5}\) and A\(\cup \)B=S (sample space), find the conditional probability P(A/B).

Part - D

Generic 5 - Answer All Question

Given P(A) = 0.4 and P(A\(\cup \)B)=0.7. Find P(B) if
(i) A and B are mutually exclusive
(ii) A and B are independent events
(iii) P(A / B) = 0.4
(iv) P(B / A) = 0.5

A factory has two machines I and II. Machine I produces 40% of items of the output and Machine II produces 60% of the items. Further 4% of items produced by Machine I are defective and 5% produced by Machine II are defective. An item is drawn at random. If the drawn item is defective, find the probability that it was produced by Machine II.

Two thirds of students in a class are boys and rest girls. It is known that the probability of a girl getting a first grade is 0.85 and that of boys is 0.70. Find the probability that a student chosen at random will get first grade marks.

Urn-I contains 8 red and 4 blue balls and urn-II contains 5 red and 10 blue balls. One urn is chosen at random and two balls are drawn from it. Find the probability that both balls are red.

Suppose the chances of hitting a target by a person X is 3 times in 4 shots, by Y is 4 times in 5 shots, and by Z is 2 times in 3 shots. They fire simultaneously exactly one time. What is the probability that the target is damaged by exactly 2 hits?

If P(A)=0.6, P(B)=0.5, and P(A\(\cap \)B)=0.2. Find
(i) P(A/B)
(ii) \(P(\bar { A } /B)\)
(iii) \(P(A/\bar { B } )\)

Two cards are drawn from a pack of 52 cards in succession. Find the probability that both are Jack when the first drawn card is (i) replaced (ii) not replaced.

Evaluate P(AUB) if 2P(A) = P(B) = \(\frac { 5 }{ 13 } \)and P(A/B) = \(\frac { 2 }{ 5 } \).
A and B are two candidates seeking admission in a college. The probability that A is selected is 0.7 and the probability that exactly one of them is selected is 0.6. Find the probability that B is selected.

A consulting firm rents car from three agencies such that 50% from agency L, 30% from agency M and 20% from agency N. If 90% of the cars from L, 70% of cars from M and 60% of the cars from N are in good conditions
(i) what is the probability that the firm will get a car in good condition?
(ii) if a car is in good condition, what is probability that it has come from agency N?

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11th Maths Monthly Test - 1 ( Introduction to probability theory )

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test - 1 ( Introduction to probability theory )-Aug 2020

Part - A

Multiple Choice Question - Answer All Question

If P(A) = 0.4, P(B) = 0.3 and P(AUB) = 0.5, then \(P(\bar { B } \cap A)\)

If A and B are two events such that P(A)= 0.4, P(B)= 0.8, and P(B/A)=0.6,then \(P(\overline{A}\cap B )\)is

If A and B are two events such that P(A) = \(\frac { 4 }{ 5 } \) and \(P(A\cap B)=\frac { 7 }{ 10 } \) then P(B/A) =

Let A and B be two events such that P(A) = 0.6, P(B) = 0.2 and P(A/B) = 0.5, Then P(\(\bar { A } /\bar { B } \)) is

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?

Out of 30 consecutive integers, 2 are chosen at random. The probability that their sum is odd is

Two dice are thrown. It is known that the sum of the numbers on the dice was less than 6, the probability of getting a sum 3 is

The probability that in a year of 22nd century, chosen at random there will be 53 Sundays is

A letter is taken at random from the letters of the word ‘ASSISTANT’ and another letter is taken at random from the letters of the word ‘STATISTICS’. The probability that the selected letters are the same is

Three integers are chosen at random from the first 20 integers. The probability that their product is even is

Part - B

Generic 2 - Answer All Question

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

Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.

Find the probability of getting the number 7, when a usual die is rolled

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 \(P(A)=0.3,P(B)=0.9,P(C)=-0.2\)

A bag contains 7 red and 4 black balls, 3 balls are drawn at random. Find the probability that (i) all are red (ii) one red and 2 black

An integer is chosen at random from the first 100 positive integers. What is the probability that the integer chosen is a prime or multiple of 8?

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

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

If two coins are tossed simultaneously, then find the probability of getting (i) one head and one tail (ii) at most two tails

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

Part - C

Generic 3 - Answer All Question

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

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

If A and B are mutually exclusive events P(A)=\(\frac{3}{8}\) and P(B)=\(\frac{1}{8}\) , then find (i) P(\(\bar { A } \)) (ii) \(P(A\cup B)\) (iii) \(P(\bar { A } \cap B)\) (iv) \(P(\bar { A } \cup \bar { B } )\)

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?

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

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

If for two events A and B, P(A)=\(\frac{3}{4}\), P(B)=\(\frac{2}{5}\) and A\(\cup \)B=S (sample space), find the conditional probability P(A/B).

Part - D

Generic 5 - Answer All Question

Given P(A) = 0.4 and P(A\(\cup \)B)=0.7. Find P(B) if (i) A and B are mutually exclusive (ii) A and B are independent events (iii) P(A / B) = 0.4 (iv) P(B / A) = 0.5

Two thirds of students in a class are boys and rest girls. It is known that the probability of a girl getting a first grade is 0.85 and that of boys is 0.70. Find the probability that a student chosen at random will get first grade marks.

Urn-I contains 8 red and 4 blue balls and urn-II contains 5 red and 10 blue balls. One urn is chosen at random and two balls are drawn from it. Find the probability that both balls are red.

Suppose the chances of hitting a target by a person X is 3 times in 4 shots, by Y is 4 times in 5 shots, and by Z is 2 times in 3 shots. They fire simultaneously exactly one time. What is the probability that the target is damaged by exactly 2 hits?

If P(A)=0.6, P(B)=0.5, and P(A\(\cap \)B)=0.2. Find (i) P(A/B) (ii) \(P(\bar { A } /B)\) (iii) \(P(A/\bar { B } )\)

Two cards are drawn from a pack of 52 cards in succession. Find the probability that both are Jack when the first drawn card is (i) replaced (ii) not replaced.

Evaluate P(AUB) if 2P(A) = P(B) = \(\frac { 5 }{ 13 } \)and P(A/B) = \(\frac { 2 }{ 5 } \).

A and B are two candidates seeking admission in a college. The probability that A is selected is 0.7 and the probability that exactly one of them is selected is 0.6. Find the probability that B is selected.

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The probability that in a year of 22^nd century, chosen at random there will be 53 Sundays is

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
\(P(A)=0.3,P(B)=0.9,P(C)=-0.2\)

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

If two coins are tossed simultaneously, then find the probability of getting
(i) one head and one tail (ii) at most two tails

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

If A and B are mutually exclusive events P(A)=\(\frac{3}{8}\) and P(B)=\(\frac{1}{8}\) , then find
(i) P(\(\bar { A } \))
(ii) \(P(A\cup B)\)
(iii) \(P(\bar { A } \cap B)\)
(iv) \(P(\bar { A } \cup \bar { B } )\)

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 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?

Given P(A) = 0.4 and P(A\(\cup \)B)=0.7. Find P(B) if
(i) A and B are mutually exclusive
(ii) A and B are independent events
(iii) P(A / B) = 0.4
(iv) P(B / A) = 0.5

If P(A)=0.6, P(B)=0.5, and P(A\(\cap \)B)=0.2. Find
(i) P(A/B)
(ii) \(P(\bar { A } /B)\)
(iii) \(P(A/\bar { B } )\)