Samacheer Kalvi solutions for Mathematics - Volume 1 and 2 [English] Class 11 TN Board chapter 12 - Introduction to probability theory [Latest edition]

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

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

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) = `2/5`, P(B) = `3/5`, P(C) = `- 1/5`, P(D) = `1/5`

If two coins are tossed simultaneously, then find the probability of getting one head and one tail

If two coins are tossed simultaneously, then find the probability of getting atmost two tails

Five mangoes and 4 apples are in a box. If two fruits are chosen at random, find the probability that one is a mango and the other is an apple

Five mangoes and 4 apples are in a box. If two fruits are chosen at random, find the probability that both are of the same variety

What is the chance that non-leap year

What is the chance that leap year should have fifty three Sundays?

Eight coins are tossed once, find the probability of getting exactly two tails

Eight coins are tossed once, find the probability of getting atleast two tails

Eight coins are tossed once, find the probability of getting atmost two tails

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?

A bag contains 7 red and 4 black balls, 3 balls are drawn at random. Find the probability that all are red

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

A single card is drawn from a pack of 52 cards. What is the probability that the card is an ace or a king

A single card is drawn from a pack of 52 cards. What is the probability that the card will be 6 or smaller

A single card is drawn from a pack of 52 cards. What is the probability that the card is either a queen or 9?

A cricket club has 16 members, of whom only 5 can bowl. What is the probability that in a team of 11 members at least 3 bowlers are selected?

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

Suppose P(B) = `2/5`. Express the odds event B occurs

If A and B are mutually exclusive events P(A) = `3/8` and P(B) = `1/8`, then find `"P"(bar"A")`

If A and B are mutually exclusive events P(A) = `3/8` and P(B) = `1/8`, then find `"P"("A" ∪ "B")`

If A and B are mutually exclusive events P(A) = `3/8` and P(B) = `1/8`, then find `"P"(bar"A" ∩ "B")`

If A and B are mutually exclusive events P(A) = `3/8` and P(B) = `1/8`, then find `"P"(bar"A" ∪ bar"B")`

If A and B are two events associated with a random experiment for which P(A) = 0.35, P(A or B) = 0.85, and P(A and B) = 0.15 Find P(only B)

If A and B are two events associated with a random experiment for which P(A) = 0.35, P(A or B) = 0.85, and P(A and B) = 0.15 Find `"P"(bar"B")` 

If A and B are two events associated with a random experiment for which P(A) = 0.35, P(A or B) = 0.85, and P(A and B) = 0.15 Find P(only A) 

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 ∪ 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 P(A ∪ 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 `"P"("A" ∩ 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 `"P"(bar"A" ∩ "B")`

A town has 2 fire engines operating independently. The probability that a fire engine is available when needed is 0.96. What is the probability that a fire engine is available when needed?

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

The probability that a new railway bridge will get an award for its design is 0.48, the probability that it will get an award for the efficient use of materials is 0.36, and that it will get both awards is 0.2. What is the probability, that it will get at least one of the two awards

The probability that a new railway bridge will get an award for its design is 0.48, the probability that it will get an award for the efficient use of materials is 0.36, and that it will get both awards is 0.2. What is the probability, that it will get only one of the awards

Can two events be mutually exclusive and independent simultaneously?

If A and B are two events such that P(A ∪ B) = 0.7, P(A ∩ B) = 0.2, and P(B) = 0.5, then show that A and B are independent

If A and B are two independent events such that P(A ∪ B) = 0.6, P(A) = 0.2, find P(B)

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

If for two events A and B, P(A) = `3/4`, P(B) = `2/5`  and A ∪ B = S (sample space), find the conditional probability P(A/B)

A problem in Mathematics is given to three students whose chances of solving it are `1/3, 1/4` and `1/5`. What is the probability that the problem is solved?

A problem in Mathematics is given to three students whose chances of solving it are `1/3, 1/4` and `1/5`. What is the probability that exactly one of them will solve it?

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. If the oil had to be changed, what is the probability that a new oil filter is needed?

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. If a new oil filter is needed, what is the probability that the oil has to be changed?

One bag contains 5 white and 3 black balls. Another bag contains 4 white and 6 black balls. If one ball is drawn from each bag, find the probability that both are white

One bag contains 5 white and 3 black balls. Another bag contains 4 white and 6 black balls. If one ball is drawn from each bag, find the probability that both are black

One bag contains 5 white and 3 black balls. Another bag contains 4 white and 6 black balls. If one ball is drawn from each bag, find the probability that one white and one black

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.

Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if A and B are mutually exclusive

Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if A and B are independent events

Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if P(A/B) = 0.4

Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if P(B/A) = 0.5

A year is selected at random. What is the probability that it contains 53 Sundays

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

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?

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?

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. find the probability that the ball is black

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. if the ball is black, what is the probability that it is from the first urn?

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, find the probability that the selected pipe is a defective one

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, if the selected pipe is a defective, then what is the probability that it was produced by plant Y?

The chances of A, B and C becoming manager of a certain company are 5 : 3 : 2. The probabilities that the office canteen will be improved if A, B, and C become managers are 0.4, 0.5 and 0.3 respectively. If the office canteen has been improved, what is the probability that B was appointed as the manager?

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 the husband is watching the television during the prime time of television

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 if the husband is watching the television, the wife is also watching the television

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Four persons are selected at random from a group of 3 men, 2 women and 4 children. The probability that exactly two of them are children is

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A number is selected from the set {1, 2, 3, ..., 20). The probability that the selected number is divisible by 3 or 4 is

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A, B, and C try to hit a target simultaneously but independently. Their respective probabilities of hitting the target are `3/4, 1/2, 5/8`. The probability that the target is hit by A or B but not by C is

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If A and B are any two events, then the probability that exactly one of them occur is

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Let A and B be two events such that `"P"(bar ("A" ∪ "B")) = 1/6, "P"("A" ∩ "B") = 1/4` and `"P"(bar"A") = 1/4`. Then the events A and B are

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Two items are chosen from a lot containing twelve items of which four are defective, then the probability that at least one of the item is defective

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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?

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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

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A matrix is chosen at random from a set of all matrices of order 2, with elements 0 or 1 only. The probability that the determinant of the matrix chosen is non zero will be

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A bag contains 5 white and 3 black balls. Five balls are drawn successively without replacement. The probability that they are alternately of different colours is

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If A and B are two events such that A ⊂ B and P(B) ≠ 0, then which of the following is correct?

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A bag contains 6 green, 2 white, and 7 black balls. If two balls are drawn simultaneously, then the probability that both are different colours is

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If X and Y be two events such that P(X/Y) = `1/2`, P(Y/X) = `1/3` and P(X ∩ Y) = `1/6`, then

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An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. The probability that the second ball drawn is red will be

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A number x is chosen at random from the first 100 natural numbers. Let A be the event of numbers which satisfies `((x  - 10)(x - 50))/(x - 30) ≥ 0`, then P(A) is

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If two events A and B are independent such that P(A) = 0.35 and P(A ∪ B) = 0.6, then P(B) is

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If two events A and B are such that `"P"(bar"A") = 3/10` and `"P"("A" ∩ bar"B") = 1/2` then P(A ∩ B) is

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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"(bar"A" ∩ "B")` is

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There are three events A, B and C of which one and only one can happen. If the odds are 7 to 4 against A and 5 to 3 against B, then odds against C is

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If a and b are chosen randomly from the set {1, 2, 3, 4} with replacement, then the probability of the real roots of the equation x² + ax + b = 0 is

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It is given that the events A and B are such that P(A) = `1/4`, P(A/B) = `1/2` and P(B/A) = `2/3`. Then P(B) is

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In a certain college 4% of the boys and 1% of the girls are taller than 1.8 meter. Further 60% of the students are girls. If a student is selected at random and is taller than 1.8 meters, then the probability that the student is a girl is

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Ten coins are tossed. The probability of getting at least 8 heads is 

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The probability of two events A and B are 0.3 and 0.6 respectively. The probability that both A and B occur simultaneously is 0.18. The probability that neither A nor B occurs is

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If m is a number such that m ≤ 5, then the probability that quadratic equation 2x² + 2mx + m + 1 = 0 has real roots is