Direction: Study the given information carefully and answer the questions that follow:

A basket contains 5 red, 4 blue, 3 green stones.

If three balls are picked at random, what is the probability that at least one is green?

Probability if at least one is Green

[1-(^{9}C_{3}/^{12}C_{3})] = 84/220 → 34/55

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Direction: Study the following information carefully and answer the questions that follow:

A committee of 10 persons is to be formed from 7 men and 6 women

In how many of these committee the men are in majority

Number of ways when men are majority in committee = ^{7}C_{6}*^{6}C_{4}+^{7}C_{7}*^{6}C_{3}

7*35+1*20 = 125

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Direction: In the following question, there are two equations. Solve the equations and answer accordingly:

**A. ** X>Y

**B. ** X ≥Y

**C. ** X
**D. ** X≤Y

**E. ** X = Y or the relationship cannot be established

**Answer : ****Option E**

**Explaination / Solution: **

I. 6x2 + 46x +60 = 0

II. 4y2+ 29y + 45= 0

II. 4y2+ 29y + 45= 0

I. 6x^{2} + 46x +60 = 0

3x^{2} + 23x + 30 = 0

3x^{2} + 18x + 5x + 30 = 0

3x(x+6)+5(x+6)=0

(x+6)(3x+5)=0

x = -5/3, -6

II. 4y^{2} + 29y + 45= 0

4y^{2} + 20y + 9y + 45= 0

4y(y+5)+9(y+5)=0

(4y+9)(y+5)=0

y = -5, -9/4

So Relationship cannot be established

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Direction: Study the following information carefully and answer the questions that follow:

A committee of 10 persons is to be formed from 7 men and 6 women.

In how many of these committee the men are in majority

Number of ways when men are majority in committee = ^{7}C_{6}*^{6}C_{4}+^{7}C_{7}*^{6}C_{3}

7*15+1*20 = 125

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Direction: Study the following information carefully and answer the questions that follow:

A committee of five members is to be formed out of 3 trainees, 4 professors and 6 engineers.

In how many ways this can be done if 1 trainees and 4 engineers be included in a committee

If 1 trainees and 4 engineers include in committee

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A black and a red dice are rolled. Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.

**A. ** 2/3

**B. ** 5/9

**C. ** 1/3

**D. ** 4/9

**Answer : ****Option C**

**Explaination / Solution: **

n(S)=36.

Let A = event of getting sum greater than 9.

= {(4,6),(5,5),(6,4),(5,6),(6,5),(6,6)}

And B = event of getting 5 on black die.

={(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)}

n(S)=36.

Let A = event of getting sum greater than 9.

= {(4,6),(5,5),(6,4),(5,6),(6,5),(6,6)}

And B = event of getting 5 on black die.

={(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)}

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Two events A and B will be independent, if

**A. ** P(A) = P(B)

**B. ** P(A) + P(B) = 1

**C. ** A and B are mutually exclusive

**D. ** P(A′B′) = [1 – P(A)] [1 – P(B)]

**Answer : ****Option D**

**Explaination / Solution: **

Two events A and B will be independent, then

Two events A and B will be independent, then

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Compute P(A|B), if P(B) = 0.5 and P (A ∩ B) = 0.32

**A. ** P(A|B) =
**B. ** P(A|B) =
**C. ** P(A|B) =
**D. ** P(A|B) =
**Answer : ****Option A**

**Explaination / Solution: **

We have , P(B) = 0.5 and P (A ∩ B) = 0.32

We have , P(B) = 0.5 and P (A ∩ B) = 0.32

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The total area under the standard normal curve is

**A. ** None of these

**B. ** 1

**C. ** 2

**D. ** 1/2

**Answer : ****Option D**

**Explaination / Solution: **

No Explaination.

No Explaination.

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Three prizes are distributed among three persons at random. The chances that none of the persons gets all the prizes is

**A. ** 6/ 216

**B. ** 210/ 216

**C. ** 120/ 216

**D. ** none of these

**Answer : ****Option B**

**Explaination / Solution: **

No Explaination.

No Explaination.

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