SSC CGL Statistics – Probability Theory – Level 3 · Challenge

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SSC CGL Statistics – Probability Theory – Level 3 · Challenge – 8 questions, subject: Statistics (Tier II Paper II). Every question has the correct answer with a one-line explanation; tap "Show Answer". Free practice for TNPSC, UPSC, SSC, Bank and RRB exams – Shanmugam IAS Academy, Coimbatore.

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1.  
Diagram-basedThe Venn diagram shows the languages read by 60 students of a fictional class.

A student who reads Hindi is chosen. What is the probability that the student also reads English?

Correct Answer: B [2/5]

Explanation:

Hindi readers = 18 + 12 = 30; of them 12 read English → 12/30 = 2/5.

2.  
A screening test detects a condition in 80% of those who have it and gives a false positive for 10% of those who do not. 5% of people have the condition. A person tests positive. The probability that the person has the condition is:

Correct Answer: D [8/27 ≈ 0.296]

Explanation:

0.04/(0.04 + 0.095) = 0.04/0.135 = 8/27 ≈ 0.296.

3.  
Machines X, Y, Z make 40%, 35% and 25% of a firm's output; 1%, 2% and 4% of their items are defective. An item is found defective. The probability that Z made it is:

Correct Answer: C [10/21]

Explanation:

Joints 0.004, 0.007, 0.010; total 0.021; 0.010/0.021 = 10/21.

4.  
P(A) = 0.6, P(B) = 0.5, P(C) = 0.4, P(A ∩ B) = 0.3, P(B ∩ C) = 0.2, P(A ∩ C) = 0.25 and P(A ∩ B ∩ C) = 0.1. The probability that exactly one of A, B, C occurs is:

Correct Answer: A [0.3]

Explanation:

ΣP − 2ΣP(pairs) + 3P(all) = 1.5 − 1.5 + 0.3 = 0.3 (A only 0.15, B only 0.1, C only 0.05).

5.  
Two-quantity comparison
Quantity I: P(at least one head in three tosses of a fair coin)
Quantity II: P(the sum of two fair dice is at least 4)

Correct Answer: B [Quantity I < Quantity II]

Explanation:

QI = 7/8 = 0.875; QII = 1 − 3/36 = 11/12 ≈ 0.917.

6.  
A speaks the truth with probability 2/3 and B with probability 5/6, independently. The probability that they contradict each other in stating the same fact is:

Correct Answer: D [7/18]

Explanation:

Exactly one truthful: (2/3)(1/6) + (1/3)(5/6) = 2/18 + 5/18 = 7/18.

7.  
The odds in favour of A are 2 : 3 and of B are 3 : 4; A and B are independent. The probability that at least one of them happens is:

Correct Answer: B [23/35]

Explanation:

P(A) = 2/5, P(B) = 3/7; 1 − (3/5)(4/7) = 1 − 12/35 = 23/35.

8.  
True/False countHow many of the following statements are true?
(i) Pairwise independence of three events implies their mutual independence.
(ii) If A ⊆ B then P(A) ≤ P(B).
(iii) P(A ∩ B) ≥ P(A) + P(B) − 1.
(iv) If A and B are independent, so are A′ and B′.

Correct Answer: A [Three]

Explanation:

(ii), (iii), (iv) true; (i) false – two coins with A, B, C = 'same faces' are pairwise but not mutually independent.

➤ Full notes, shortcuts and every answer explained – SSC CGL 2026 Statistics (Tier II Paper II) book (₹149): www.shanmugamiasacademy.in/study-materials/ssc-cgl-statistics

📘 SSC CGL 2026 – Statistics (Tier II Paper II)
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