Probability Test

Result

Probability Test - 4

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Score
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Rank

Time Taken: -

Question 1/3
1 / -0

A number is chosen randomly from the set {1, 2, 3, …15}. If chosen number is a two digit number, then the probability that the number is a prime numbers, is

Correct

Wrong

Skipped
A
1/2

Correct

Wrong

Skipped
B
1/3

Correct

Wrong

Skipped
C
1/4

Correct

Wrong

Skipped
D
1/5

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Solutions

Required probability = 2 / 6 = 1/3
Hence, option B is correct.
Question 2/3
1 / -0

A single letter is selected at random from the word 'PROBABILITY'. The probability that it is a vowel is –

Correct

Wrong

Skipped
A
3/11

Correct

Wrong

Skipped
B
2/11

Correct

Wrong

Skipped
C
4/11

Correct

Wrong

Skipped
D
7/11

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Solutions

PROBABILITY
vowel = O, A, I, I
Total case = ¹¹C₁ = 11
Favourable case = ⁴C₁ = 4
Required probability = 4/11
Question 3/3
1 / -0

Let A, B, C be three mutually independent events. Consider the two statements S₁ and S₂
S₁ : A and B ∪ C are independent
S₂ : A and B ∩ C are independent
Then,

Correct

Wrong

Skipped
A
Both S₁ and S₂ are true

Correct

Wrong

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B
Only S₁ is true

Correct

Wrong

Skipped
C
Only S₂ is true

Correct

Wrong

Skipped
D
Neither S₁ nor S₂ is true

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Solutions

We are given that

P(A ∩ B) = P(A) P(B)
P(B ∩ C) = P(B) P(C), P(C ∩ A) = P(C) P(A)
And P( A ∩ B ∩ C)=P(A) P(B) P(C)
=P(A) P(B) P(C) = P(A) P(B ∩ C).
⟹ A and B ∩ C are independent. Therefore, S2 is true.
Also P[(A ∩ (B ∪ C)]= P[(A ∩ B) ∪ (A ∩ C)]
=P(A ∩B) + P(A ∩ C) –P[A ∩ B) ∩ (A ∩ C)]
=P(A ∩ B) + P(A ∩ C) – P(A ∩ B ∩ C)

=P(A) P(B) +P(A) P(C) – P(A) P(B) P(C)
=P(A) [P(B) +P(C)-P(B) P(C)]
=P(A) [P(B) + P(C) –P(B ∩ C)] = P(A) P(B ∪ C)
∴ A and B ∪ C are independent.

Question 1/3

1/2

1/3

1/4

1/5

Question 2/3

3/11

2/11

4/11

7/11

Question 3/3

Both S₁ and S₂ are true

Only S₁ is true

Only S₂ is true

Neither S₁ nor S₂ is true

Question 1/3

1/2

1/3

1/4

1/5

Question 2/3

3/11

2/11

4/11

7/11

Question 3/3

Both S1 and S2 are true

Only S1 is true

Only S2 is true

Neither S1 nor S2 is true

Both S₁ and S₂ are true

Only S₁ is true

Only S₂ is true

Neither S₁ nor S₂ is true