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GATE 2024 CE (CE1) – Question 13

Engineering Mathematics · Probability and Statistics: Probability, conditional probability, descriptive statistics · 1 mark · Multiple choice

The probability that a student passes only in Mathematics is $\frac{1}{3}$. The probability that the student passes only in English is $\frac{4}{9}$. The probability that the student passes in both of these subjects is $\frac{1}{6}$. The probability that the student will pass in at least one of these two subjects is

  1. $\frac{17}{18}$
  2. $\frac{11}{18}$
  3. $\frac{14}{18}$
  4. $\frac{1}{18}$

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Correct answer: (A) $\frac{17}{18}$

Explanation

The three cases (only Mathematics, only English, both) are mutually exclusive and together make up "at least one": $\frac{1}{3} + \frac{4}{9} + \frac{1}{6} = \frac{6 + 8 + 3}{18} = \frac{17}{18}$.