# Probability and Statistics Probability and Statistics
| Probability and Statistics | | Probability | | Statistics |
Q.1
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?
A. 1/15
B. 1/11
C. 3/16
D. 1/13
E. None of these
Answer : Option B
Explaination / Solution:

Probability if both is blue
4C2/12C2 = 6/66 → 1/11

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Q.2

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

A. 45
B. 35
C. 110
D. 56
E. None of these
Answer : Option B
Explaination / Solution:

Number of ways when women are majority in committee = 6C6*7C4 = 1*35 = 35

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Q.3
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
x = (-7/4, -2)
II. 9y2 + 11y+2 =0
y = (-1, -2/9)
So x<y

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Q.4
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.
A. 251
B. 265
C. 167
D. 340
E. None of these
Answer : Option A
Explaination / Solution:

Number of Ways when if at least 5 men include in committee = 7C5*6C5+7C6*6C4+7C7*6C3
= 21*6+7*15+1*20
= 251

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Q.5
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
A. 32
B. 60
C. 45
D. 90
E. None of these
Answer : Option B
Explaination / Solution:

If 2 trainees and 3 engineers include in committee
3C2*6C3 = 3*20 --> 60

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Q.6
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
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Q.7

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

A. P(A) = P(E1) P (A|E1) + P (E2) P (A|E2) + ... + P (En) P(A|En)
B. P(A) = P(E1) P (A|E1) + P (E1) P (A|E2) + ... + P (En) P(A|En)
C. P(A) = P(E0) P (A|E1) + P (E1) P (A|E2) + ... + P (En – 1) P(A|En)
D. P(A) = P(E2) P (A|E1) + P (E2) P (A|E2) + ... + P (En) P(A|En)
Answer : Option A
Explaination / Solution:

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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Q.8

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

A. 0.22
B. 0.24
C. 0
D. 0.25
Answer : Option C
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Q.9
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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Q.10
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.

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