CUET UG 2025 — General Test Quantitative Reasoning

The bag contains:

• Red balls: 3
• Blue balls: 2
• Green balls: 5
• Yellow balls: 4

Total balls:

$$3 + 2 + 5 + 4 = 14$$3+2+5+4=14

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The total number of ways to pick 2 balls from 14 balls:

$$C(14, 2) = \dfrac{14 \times 13}{2}$$C(14,2)=214×13​

$$= \dfrac{182}{2}$$=2182​

$$= 91$$=91

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For both balls to be red, the number of ways to pick 2 red balls from 3 red balls:

$$C(3, 2) = \dfrac{3 \times 2}{2} = 3$$C(3,2)=23×2​=3

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For both balls to be blue, the number of ways to pick 2 blue balls from 2 blue balls:

$$C(2, 2) = 1$$C(2,2)=1

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Total favorable outcomes:

$$3 + 1 = 4$$3+1=4

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The probability that either both are red or both are blue:

$$P = \dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}$$P=Total outcomesFavorable outcomes​

$$= \dfrac{4}{91}$$=914​

Therefore, the probability is $\dfrac{4}{91}$914​.