SSC CGL Statistics – Probability Theory – Exam-Level Drill

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SSC CGL Statistics – Probability Theory – Exam-Level Drill – 10 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.  

Directions (Q 36–39): A fictional courier sends 45% of its parcels by Route X, 35% by Route Y and 20% by Route Z. Of these, 4%, 6% and 10% respectively arrive late.

What is the probability that a parcel chosen at random arrives late?

Correct Answer: D [0.059]

Explanation:

0.45 × 0.04 + 0.35 × 0.06 + 0.20 × 0.10 = 0.018 + 0.021 + 0.020 = 0.059.

2.  
(Use the directions above – Q 36–39)
A parcel arrives late. What is the probability that it went by Route Z?

Correct Answer: C [20/59]

Explanation:

Answer: 20/59. 0.020/0.059 = 20/59 ≈ 0.339.

3.  
(Use the directions above – Q 36–39)
A parcel arrives on time. What is the probability that it went by Route X (to three decimals)?

Correct Answer: B [0.459]

Explanation:

0.45 × 0.96/(1 − 0.059) = 0.432/0.941 ≈ 0.459.

4.  
(Use the directions above – Q 36–39)
For a late parcel, which route is the most likely?

Correct Answer: C [Route Y]

Explanation:

Joint probabilities: X 0.018, Y 0.021, Z 0.020 – Y is largest.

5.  
Two fair dice are rolled. The probability that the sum is a multiple of 3 is:

Correct Answer: B [1/3]

Explanation:

Sums 3, 6, 9, 12 have 2 + 5 + 4 + 1 = 12 ways (Two-Dice Triangle) → 12/36 = 1/3.

6.  
P(A) = 1/3, P(B) = 1/4 and P(A ∪ B) = 1/2. Which statement is correct?

Correct Answer: A [P(A ∣ B) = 1/3 and A, B are independent]

Explanation:

P(A ∩ B) = 1/3 + 1/4 − 1/2 = 1/12 = P(A)P(B); P(A ∣ B) = (1/12)/(1/4) = 1/3.

7.  
A committee of 3 is chosen at random from 5 men and 4 women. The probability that it has at least one woman is:

Correct Answer: D [37/42]

Explanation:

1 − C(5, 3)/C(9, 3) = 1 − 10/84 = 37/42.

8.  
Three people are each equally likely to have been born on any day of the week, independently. The probability that all three were born on different days is:

Correct Answer: C [30/49]

Explanation:

(7 × 6 × 5)/7³ = 210/343 = 30/49.

9.  
Two fair dice are rolled and the sum is known to be 10. The probability that both numbers are even is:

Correct Answer: D [2/3]

Explanation:

Reduced space (4,6), (5,5), (6,4); two have both even → 2/3.

10.  
P(A) = 0.75 and P(B) = 0.65. The smallest possible value of P(A ∩ B) is:

Correct Answer: B [0.4]

Explanation:

P(A ∩ B) ≥ P(A) + P(B) − 1 = 0.4 (attained when A ∪ B = S).

➤ 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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