11th Maths Monthly Test - 4 ( Introduction to probability theory )

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test - 4 ( Introduction to probability theory )-Aug 2020

Time : 2.00 Hours

Part - A

Generic 5 - Answer All Question

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.

If P(A) =0.5, P(B) =0.8 and P(B/A) = 0.8, find P(A/B) and P(A\(\cup \)B)

An advertising executive is studying television viewing habits of married men and women during prime time hours. Based on the past viewing records he has determined that during prime time wives are watching television 60% of the time. It has also been determined that when the wife is watching television, 40% of the time the husband is also watching. When the wife is not watching the television, 30% of the time the husband is watching the television. Find the probability that
(i) the husband is watching the television during the prime time of television
(ii) if the husband is watching the television, the wife is also watching the television

X speaks truth in 70 percent of cases, and Y in 90 percent of cases. What is the probability that they likely to contradict each other in stating the same fact?

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. If an item is drawn at random, find the probability that it is a defective item.

A year is selected at random. What is the probability that
(i) it contains 53 Sundays
(ii) it is a leap year which contains 53 Sundays.

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 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.

for a loaded die, the probabilities of outcomes are given as under
P(1) = P(2) = \(\frac { 2 }{ 10 } \), P(3) = P(5) = P(6) = \(\frac { 1 }{ 10 } \) and P(4) = \(\frac { 3 }{ 10 } \)
The die is thrown 2 times. Let A and B be the events as defined below
A: Getting same number each time
B: Getting a total score of 10 or more
Discuss the independency of the events A and B

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

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

The probability of simultaneous occurrence of atleast one of two events A and B is p. if the probability that exactly one A, B occurs is q then prove that P(\(\bar { A } \)) + P(\(\bar { B } \)) = 2-2 p+q.

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11th Maths Monthly Test - 4 ( Introduction to probability theory )

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test - 4 ( Introduction to probability theory )-Aug 2020

Part - A

Generic 5 - Answer All Question

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.

If P(A) =0.5, P(B) =0.8 and P(B/A) = 0.8, find P(A/B) and P(A\(\cup \)B)

X speaks truth in 70 percent of cases, and Y in 90 percent of cases. What is the probability that they likely to contradict each other in stating the same fact?

A year is selected at random. What is the probability that (i) it contains 53 Sundays (ii) it is a leap year which contains 53 Sundays.

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 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.

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

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

The probability of simultaneous occurrence of atleast one of two events A and B is p. if the probability that exactly one A, B occurs is q then prove that P(\(\bar { A } \)) + P(\(\bar { B } \)) = 2-2 p+q.

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A year is selected at random. What is the probability that
(i) it contains 53 Sundays
(ii) it is a leap year which contains 53 Sundays.

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.

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