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GATE 2016 CE (CE2) – Question 14

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

X and Y are independent events with $P(X)=0.40$ and $P(X\cup Y^c)=0.7$. What is $P(X\cup Y)$?

  1. 0.7
  2. 0.5
  3. 0.4
  4. 0.3

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Correct answer: (A) 0.7

Explanation

Let p=P(Y). Independence also holds between X and the complement of Y. Hence P(X union Y-complement)=0.4+(1−p)−0.4(1−p)=1−0.6p=0.7, giving p=0.5. Then P(X union Y)=0.4+0.5−0.4·0.5=**0.7, A**.