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

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

If two stones are picked at random, what is the probability that both are blue?

Probability if both is blue

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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 ways of these committee the women are in majority

Number of ways when women are majority in committee =

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Directions: In the following questions two equations numbered I and II are given. You have to solve both the equations.

I. 8x2 + 30x + 28 = 0

II. 9y2 + 11y+2 =0

**A. ** X>Y

**B. ** X ≥Y

**C. ** X
**D. ** X≤Y

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

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

**Explaination / Solution: **

I. 8x2 + 30x + 28 = 0

II. 9y2 + 11y+2 =0

I. 8x^{2} + 30x + 28 = 0

x = (-7/4, -2)

II. 9y^{2} + 11y+2 =0

y = (-1, -2/9)

So x<y

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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 ways this can be done if at least 5 men to have to be included in a committee.

Number of Ways when if at least 5 men include in committee = ^{7}C_{5}*^{6}C_{5}+^{7}C_{6}*^{6}C_{4}+^{7}C_{7}*^{6}C_{3}

= 21*6+7*15+1*20

= 251

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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 2 trainees and 3 engineer to have to be included in a committee

If 2 trainees and 3 engineers include in committee

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A coin is tossed three times, if E : head on third toss , F : heads on first two tosses. Find P(E|F)

**A. ** 1/5

**B. ** 1/2

**C. ** 1/3

**D. ** 2/3

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

**Explaination / Solution: **

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Let ( be a partition of a sample space and suppose that each of has nonzero probability. Let A be any event associated with S,then

Let {E1, E2, ...,En) be a partition of a sample space and suppose that each of E1, E2, ..., En has nonzero probability. Let A be any event associated with S,then P(A) = P(E1) P (A|E1) + P (E2) P (A|E2) + ... + P (En) P(A|En) .by addition law of probability.

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Two coins are tossed once ,where E :no tail appears , F : no head appers. Find P(E/F).

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A dice is rolled 6 times. The probability of obtaining 2 and 4 exactly three times each is

**A. ** none of these

**B. ** 1/ 46656

**C. ** 1/ 5184

**D. ** 5/ 11664

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

**Explaination / Solution: **

Total ways of getting 2 and 4 exactly 3 times is 6! / (3! 3!) = 20

Total number of ways in throwing 6 dice is 66

Therefore probability is 20/ 66 = 5/11664

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In a certain town , 40% persons have brown hair , 25% have brown eyes , and 15% have both. If a person selected at random has brown hair , the chance that a person selected at random with brown hair is with brown eyes

**A. ** 3/20

**B. ** 2/3

**C. ** 3/8

**D. ** 1/3

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

**Explaination / Solution: **

No Explaination.

No Explaination.

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