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

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

If two balls are picked at random, what is the probability that either both are red or both are blue?

Probabilities if both either are Red or either are blue

= (^{5}C_{2} + ^{4}C_{2})/^{12}C_{2} = (10+6)/66 → 8/33

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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 6 men and 4 women be included in a committee

If 6 men and 4 women include 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. 8x – y = 40

II. 4x + y = 32

**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: **

After solving the both equation got values of x = 6 and y = 8 So X

I. 8x – y = 40

II. 4x + y = 32

After solving the both equation got values of x = 6 and y = 8 So X

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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 6 men and 4 women be included in a committee

If 6 men and 4 women include in committee =

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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 3 engineers and 2 professors or 2 trainees and 3 professor be included in a committee

If 3 engineers and 2 professors or 2 trainees and 3 professors include in committee

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A black and a red dice are rolled. Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.

**A. ** 1/9

**B. ** 4/9

**C. ** 5/9

**D. ** 7/9

**Answer : ****Option A**

**Explaination / Solution: **

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If P(A) = and P(B) = , find P (A ∩ B) if A and B are independent events.

**A. ** 4/25

**B. ** 3/25

**C. ** 7/25

**D. ** 8/25

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

**Explaination / Solution: **

Since A and B are independent events .

Therefore ,

Since A and B are independent events .

Therefore ,

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If P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4, find P(A ∩ B)

**A. ** 0.32

**B. ** 0.29

**C. ** 0.35

**D. ** 0.37

**Answer : ****Option A**

**Explaination / Solution: **

We have ,

P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4

We have ,

P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4

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Neelam and Nidhi throw with a dice .The chance that both Neelam and Nidhi throw the same number is

**A. ** 1/ 6

**B. ** none of these

**C. ** 1/ 36

**D. ** 1/ 2

**Answer : ****Option A**

**Explaination / Solution: **

TOTAL NO. OF OUTCOMES=62=36

no. of outcomes in which both throws same no.={(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)}=6

p(both throws same no.)=6/36=1/6

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The letters of the word ‘ MALENKOV ‘are arranged in all possible ways. The chance that there are exactly four letters between M and E is

**A. ** 3/ 14

**B. ** 1/ 14

**C. ** None of these

**D. ** 3/28

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

**Explaination / Solution: **

No Explaination.

No Explaination.

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