11th Maths Weekly Test - 2 ( Introduction to probability theory )

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test - 2 ( Introduction to probability theory )-Aug 2020

Time : 1.30 Hours

Part - A

Generic 2 - Answer All Question

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

A factory has two Machines-I and II. Machine-I produces 60% of items and Machine-II produces 40% of the items of the total output. Further 2% of the items produced by Machine-I are defective whereas 4% produced by Machine-II are defective. If an item is drawn at random what is the probability that it is defective?

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
\(P(A)=\frac { 2 }{ 5 } ,\quad P(B)=\frac { 1 }{ 5 } ,\quad P(C)=\frac { 3 }{ 5 } \)

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
\(P(A)=\frac { 4 }{ 7 } ,P(B)=\frac { 1 }{ 7 } ,P(C)=\frac { 2 }{ 7 } \)

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.

What is the chance that (i) non-leap year (ii) leap year should have fifty three Sundays?

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

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) = 0.15, P(B) = 0.30, P(C) = 0.43 , P(D)= 0.12

A man has 2 ten rupee notes, 4 hundred rupee notes and 6 five hundred rupee 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 and also its probability

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

Part - B

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 couple has two children. Find the probability that
(i) both the children are boys, if it is known that the older child is a boy.
(ii) both the children are girls, if it is known that the older child is a girl.

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.

In answering a question on a multiple choice test, a student either knows the answer or guesses. Let \(\frac { 3 }{ 4 } \) be the probability that he knows the answer and \(\frac { 1 }{ 4 } \) be the probability that he guesses. Assuming that a student who guesse at the answer will be correct with probability \(\frac { 1 }{ 4 } \). What is the probability that the student knows the answer given that he answered it correctly?

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11th Maths Weekly Test - 2 ( Introduction to probability theory )

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test - 2 ( Introduction to probability theory )-Aug 2020

Part - A

Generic 2 - Answer All Question

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

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 \(P(A)=\frac { 2 }{ 5 } ,\quad P(B)=\frac { 1 }{ 5 } ,\quad P(C)=\frac { 3 }{ 5 } \)

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 \(P(A)=\frac { 4 }{ 7 } ,P(B)=\frac { 1 }{ 7 } ,P(C)=\frac { 2 }{ 7 } \)

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.

What is the chance that (i) non-leap year (ii) leap year should have fifty three Sundays?

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

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) = 0.15, P(B) = 0.30, P(C) = 0.43 , P(D)= 0.12

A man has 2 ten rupee notes, 4 hundred rupee notes and 6 five hundred rupee 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 and also its probability

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

Part - B

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 couple has two children. Find the probability that (i) both the children are boys, if it is known that the older child is a boy. (ii) both the children are girls, if it is known that the older child is a girl.

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.

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

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
\(P(A)=\frac { 2 }{ 5 } ,\quad P(B)=\frac { 1 }{ 5 } ,\quad P(C)=\frac { 3 }{ 5 } \)

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
\(P(A)=\frac { 4 }{ 7 } ,P(B)=\frac { 1 }{ 7 } ,P(C)=\frac { 2 }{ 7 } \)

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

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) = 0.15, P(B) = 0.30, P(C) = 0.43 , P(D)= 0.12

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 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 couple has two children. Find the probability that
(i) both the children are boys, if it is known that the older child is a boy.
(ii) both the children are girls, if it is known that the older child is a girl.