• Your ability to analyze uncertain situations

• Understanding of basic and conditional probability

• Skills in solving real-world scenario-based problems

This page covers all probability PYQs with smart calculation techniques.

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Year-Wise Probability PYQs (2011-2024)

Q1. A round archery target of diameter 1 m is marked with four scoring regions from the centre outwards as red, blue, yellow and white. The radius of the red band is 0.20 m. The width of all the remaining bands is equal. If archers throw arrows towards the target, what is the probability that the arrows fall in the red region of the archery target? [CSAT 2016]

(a) 0.40

(b) 0.20

(c) 0.16

(d) 0.04

Solution:

Given that,

A around archery target of diameter 1 m is marked with four scoring regions from the centre outwards as red, blue, yellow and white.

The radius of the red band is 0.20 m.

The width of all the remaining bands is equal.

Now,

The area of red band = π(0.20)² = 0.04 π

Radius of round archery target = 1/2 = 0.5m

Total area = π(0.5)²= 0.25 π

Probability = 0.04 π/0.25 π = 0.16

Hence option (c) is correct

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Q2. A bag contains 15 red balls and 20 black balls. Each ball is numbered either 1 or 2 or 3. 20% of the red balls are numbered 1 and 40% of them are numbered 3. Similarly, among the black balls, 45% are numbered 2 and 30% are numbered 3. A boy picks a ball at random. He wins if the ball is red and numbered 3 or if it is black and numbered 1 or 2. What are the chances of his winning? [CSAT 2018]

(a) 1/2

(b) 4/7

(c) 5/9

(d) 12/13

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