The GATE Grind

GATE 2026 IN – Question 36

Engineering Mathematics · Probability and statistics · 2 marks · Multiple choice

A box contains three apples and two oranges. Two fruits are removed randomly in succession. The probability that the first is an apple and the second is an orange is ________.

  1. $\frac35$
  2. $\frac3{20}$
  3. $\frac3{10}$
  4. $\frac25$

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Show answer and explanation

Correct answer: (C) $\frac3{10}$

Explanation

The probability of an apple on the first draw is $3/5$. After an apple is removed without replacement, two oranges remain among four fruits, so the conditional probability of an orange is $2/4$.

Multiplying gives $(3/5)(2/4)=3/10$, **option C**.