SSC CGL Statistics – Probability Theory – Level 2 · Exam Level · Paper II Sprint

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SSC CGL Statistics – Probability Theory – Level 2 · Exam Level · Paper II Sprint – 15 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.  
Two dice are rolled. The probability that the product of the two numbers is 18 is:

Correct Answer: C [1/18]

Explanation:

(3, 6) and (6, 3) → 2/36 = 1/18.

2.  
P(A) = 0.6, P(B) = 0.5 and P(A ∪ B) = 0.8. Find P(A ∩ B).

Correct Answer: A [0.3]

Explanation:

Answer: 0.3. 0.6 + 0.5 − 0.8 = 0.3.

3.  
P(A ∩ B) = 0.18 and P(A) = 0.45. Find P(B ∣ A).

Correct Answer: B [0.4]

Explanation:

Answer: 0.4. 0.18/0.45 = 0.4.

4.  
A bag has 4 white and 6 black balls. Two balls are drawn without replacement. The probability that both are black is:

Correct Answer: D [1/3]

Explanation:

Answer: 1/3. (6/10)(5/9) = 30/90 = 1/3.

5.  
A fair die is thrown three times. The probability of getting a number less than 3 at least once is:

Correct Answer: C [19/27]

Explanation:

P(no 1 or 2 in a throw) = 4/6 = 2/3; 1 − (2/3)³ = 1 − 8/27 = 19/27.

6.  
A non-leap year is chosen at random. The probability that it has 53 Mondays is:

Correct Answer: D [1/7]

Explanation:

365 days = 52 weeks + 1 extra day; that day is a Monday with probability 1/7.

7.  
Two-quantity comparisonTwo fair dice are thrown:
Quantity I: P(sum = 7)
Quantity II: P(sum = 8)

Correct Answer: A [Quantity I > Quantity II]

Explanation:

Answer: Quantity I > Quantity II. 6/36 against 5/36.

8.  
Assertion–Reason
A: If A and B are independent, then A and B′ are also independent.
R: P(A ∩ B′) = P(A) − P(A ∩ B) = P(A) − P(A)P(B) = P(A)P(B′).

Correct Answer: A [Both A and R are true and R explains A]

Explanation:

Answer: Both A and R are true and R explains A. The algebra in R proves A.

9.  
Odd one outwhich of these can NOT be the probability of an event?

Correct Answer: B [6/5]

Explanation:

Probabilities lie between 0 and 1.

10.  
A and B are independent with P(A) = 0.6 and P(B) = 0.3. The probability that exactly one of them occurs is:

Correct Answer: A [0.54]

Explanation:

0.6 × 0.7 + 0.4 × 0.3 = 0.42 + 0.12 = 0.54.

11.  
Box I has 3 red and 2 blue balls; Box II has 1 red and 4 blue. A box is chosen at random and a ball drawn from it is red. The probability that it came from Box I is:

Correct Answer: B [3/4]

Explanation:

(½ × 3/5)/(½ × 3/5 + ½ × 1/5) = 0.3/0.4 = 3/4.

12.  
Spot My Mistake“A and B are independent, P(A) = 0.4, P(B) = 0.5, so P(A ∪ B) = 0.9.” What is the correct P(A ∪ B)?

Correct Answer: C [0.7]

Explanation:

Answer: 0.7. 0.4 + 0.5 − 0.4 × 0.5 = 0.7.

13.  
Two cards are drawn from a pack of 52 without replacement. The probability that both are hearts is:

Correct Answer: D [1/17]

Explanation:

(13/52)(12/51) = 156/2652 = 1/17.

14.  
Three independent events have probabilities 0.2, 0.5 and 0.6. The probability that at least one of them occurs is:

Correct Answer: A [0.84]

Explanation:

P(none) = 0.8 × 0.5 × 0.4 = 0.16; 1 − 0.16 = 0.84.

15.  
Statement-basedWhich of the following is/are correct?
I. P(A ∣ B) = P(B ∣ A) for all events A and B.
II. Two mutually exclusive events with positive probabilities cannot be independent.

Correct Answer: C [Only II]

Explanation:

P(A∣B) = P(B∣A) only when P(A) = P(B); exclusive events with positive probability have P(A ∩ B) = 0 ≠ P(A)P(B).

➤ 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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