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MAT Exam 2025 Paper

Question : 72 of 150

Marks: +1, -0

Solution:

Concept:

Use the inclusion-exclusion principle and the formula for probability.

Explanation:

Total tickets from 51 to 80 are:

80 - 51 + 1 = 30

Numbers divisible by 3 from 51 to 78:

\frac{78 - 51}{3} + 1 = 10

Numbers divisible by 5 from 55 to 80:

\frac{80 - 55}{5} + 1 = 6

Numbers divisible by both 3 and 5 are multiples of 15, from 60 to 75:

\frac{75 - 60}{15} + 1 = 2

Favorable outcomes:

10 + 6 - 2 = 14

Probability:

\text{Probability} = \frac{14}{30} = \frac{7}{15}

Answer:

\frac{7}{15}

, i.e., Option C.

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